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Journal articles on the topic 'Banach space'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2023

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1

Jordá, Enrique. "Weighted Vector-Valued Holomorphic Functions on Banach Spaces." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/501592.

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We study the weighted Banach spaces of vector-valued holomorphic functions defined on an open and connected subset of a Banach space. We use linearization results on these spaces to get conditions which ensure that a functionfdefined in a subsetAof an open and connected subsetUof a Banach spaceX, with values in another Banach spaceE, and admitting certain weak extensions in a Banach space of holomorphic functions can be holomorphically extended in the corresponding Banach space of vector-valued functions.

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2

Alvarez, Teresa, Manuel Gonzalez, and Victor M. Onieva. "Totally Incomparable Banach Spaces and Three-Space Banach Space Ideals." Mathematische Nachrichten 131, no. 1 (1987): 83–88. http://dx.doi.org/10.1002/mana.19871310108.

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3

Robbins, D. A. "Some extremal properties of section spaces of Banach bundles and their duals." International Journal of Mathematics and Mathematical Sciences 29, no. 10 (2002): 563–72. http://dx.doi.org/10.1155/s0161171202008086.

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WhenXis a compact Hausdorff space andEis a real Banach space there is a considerable literature on extremal properties of the spaceC(X,E)of continuousE-valued functions onX. What happens if the Banach spaces in which the functions onXtake their values vary overX? In this paper, we obtain some extremal results on the section spaceΓ(π)and its dualΓ(π)*of a real Banach bundleπ:ℰ→X(with possibly varying fibers), and point out the difficulties in arriving at totally satisfactory results.

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4

Agud, Lucia, Jose Manuel Calabuig, Maria Aranzazu Juan, and Enrique A. Sánchez Pérez. "Banach Lattice Structures and Concavifications in Banach Spaces." Mathematics 8, no. 1 (January 14, 2020): 127. http://dx.doi.org/10.3390/math8010127.

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Let ( Ω , Σ , μ ) be a finite measure space and consider a Banach function space Y ( μ ) . We say that a Banach space E is representable by Y ( μ ) if there is a continuous bijection I : Y ( μ ) → E . In this case, it is possible to define an order and, consequently, a lattice structure for E in such a way that we can identify it as a Banach function space, at least regarding some local properties. General and concrete applications are shown, including the study of the notion of the pth power of a Banach space, the characterization of spaces of operators that are isomorphic to Banach lattices of multiplication operators, and the representation of certain spaces of homogeneous polynomials on Banach spaces as operators acting in function spaces.

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5

Ghosh, P., and T. K. Samanta. "Об устойчивости ретро банахова фрейма относительно b-линейного функционала в n-банаховом пространстве." Владикавказский математический журнал, no. 1 (March 23, 2023): 48–63. http://dx.doi.org/10.46698/o3961-3328-9819-i.

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We introduce the notion of a retro Banach frame relative to a bounded $b$-linear functional in $n$-Banach space and see that the sum of two retro Banach frames in $n$-Banach space with different reconstructions operators is also a retro Banach frame in $n$-Banach space. Also, we define retro Banach Bessel sequence with respect to a bounded $b$-linear functional in $n$-Banach space. A necessary and sufficient condition for the stability of retro Banach frame with respect to bounded $b$-linear functional in $n$-Banach space is being obtained. Further, we prove that retro Banach frame with respect to bounded $b$-linear functional in $n$-Banach space is stable under perturbation of frame elements by positively confined sequence of scalars. In $n$-Banach space, some perturbation results of retro Banach frame with the help of bounded $b$-linear functional in $n$-Banach space have been studied. Finally, we give a sufficient condition for finite sum of retro Banach frames to be a retro Banach frame in $n$-Banach space. At the end, we discuss retro Banach frame with respect to a bounded $b$-linear functional in Cartesian product of two $n$-Banach spaces.

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Morris, Sidney A., and David T. Yost. "Observations on the Separable Quotient Problem for Banach Spaces." Axioms 9, no. 1 (January 13, 2020): 7. http://dx.doi.org/10.3390/axioms9010007.

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The longstanding Banach–Mazur separable quotient problem asks whether every infinite-dimensional Banach space has a quotient (Banach) space that is both infinite-dimensional and separable. Although it remains open in general, an affirmative answer is known in many special cases, including (1) reflexive Banach spaces, (2) weakly compactly generated (WCG) spaces, and (3) Banach spaces which are dual spaces. Obviously (1) is a special case of both (2) and (3), but neither (2) nor (3) is a special case of the other. A more general result proved here includes all three of these cases. More precisely, we call an infinite-dimensional Banach space X dual-like, if there is another Banach space E, a continuous linear operator T from the dual space E * onto a dense subspace of X, such that the closure of the kernel of T (in the relative weak* topology) has infinite codimension in E * . It is shown that every dual-like Banach space has an infinite-dimensional separable quotient.

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7

Folch-Gabayet, Magali, Martha Guzmán-Partida, and Salvador Pérez-Esteva. "Lipschitz measures and vector-valued Hardy spaces." International Journal of Mathematics and Mathematical Sciences 25, no. 5 (2001): 345–56. http://dx.doi.org/10.1155/s0161171201004549.

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We define certain spaces of Banach-valued measures called Lipschitz measures. When the Banach space is a dual spaceX*, these spaces can be identified with the duals of the atomic vector-valued Hardy spacesHXp(ℝn),0<p<1. We also prove that all these measures have Lipschitz densities. This implies that for every real Banach spaceXand0<p<1, the dualHXp(ℝn)∗can be identified with a space of Lipschitz functions with values inX*.

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8

Kusraev, Anatoly, and Semën Kutateladze. "Geometric Characterization of Injective Banach Lattices." Mathematics 9, no. 3 (January 27, 2021): 250. http://dx.doi.org/10.3390/math9030250.

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This is a continuation of the authors’ previous study of the geometric characterizations of the preduals of injective Banach lattices. We seek the properties of the unit ball of a Banach space which make the space isometric or isomorphic to an injective Banach lattice. The study bases on the Boolean valued transfer principle for injective Banach lattices. The latter states that each such lattice serves as an interpretation of an AL-space in an appropriate Boolean valued model of set theory. External identification of the internal Boolean valued properties of the corresponding AL-spaces yields a characterization of injective Banach lattices among Banach spaces and ordered Banach spaces. We also describe the structure of the dual space and present some dual characterization of injective Banach lattices.

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9

Tan, Dongni, and Xujian Huang. "The wigner property for CL-spaces and finite-dimensional polyhedral Banach spaces." Proceedings of the Edinburgh Mathematical Society 64, no. 2 (April 30, 2021): 183–99. http://dx.doi.org/10.1017/s0013091521000079.

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AbstractWe say that a map $f$ from a Banach space $X$ to another Banach space $Y$ is a phase-isometry if the equality \[ \{\|f(x)+f(y)\|, \|f(x)-f(y)\|\}=\{\|x+y\|, \|x-y\|\} \]holds for all $x,\,y\in X$. A Banach space $X$ is said to have the Wigner property if for any Banach space $Y$ and every surjective phase-isometry $f : X\rightarrow Y$, there exists a phase function $\varepsilon : X \rightarrow \{-1,\,1\}$ such that $\varepsilon \cdot f$ is a linear isometry. We present some basic properties of phase-isometries between two real Banach spaces. These enable us to show that all finite-dimensional polyhedral Banach spaces and CL-spaces possess the Wigner property.

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10

Soybaş, Danyal. "The () Property in Banach Spaces." Abstract and Applied Analysis 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/754531.

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A Banach space is said to have (D) property if every bounded linear operator is weakly compact for every Banach space whose dual does not contain an isomorphic copy of . Studying this property in connection with other geometric properties, we show that every Banach space whose dual has (V∗) property of Pełczyński (and hence every Banach space with (V) property) has (D) property. We show that the space of real functions, which are integrable with respect to a measure with values in a Banach space , has (D) property. We give some other results concerning Banach spaces with (D) property.

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11

Fleming, R. J., and J. E. Jamison. "Hermitian operators and isometries on sums of Banach spaces." Proceedings of the Edinburgh Mathematical Society 32, no. 2 (June 1989): 169–91. http://dx.doi.org/10.1017/s0013091500028583.

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Let E be a Banach sequence space with the property that if (αi) ∈ E and |βi|≦|αi| for all i then (βi) ∈ E and ‖(βi)‖E≦‖(αi)‖E. For example E could be co, lp or some Orlicz sequence space. If (Xn) is a sequence of real or complex Banach spaces, then E can be used to construct a vector sequence space which we will call the E sum of the Xn's and symbolize by ⊕EXn. Specifically, ⊕EXn = {(xn)|(xn)∈Xn and (‖xn‖)∈E}. The E sum is a Banach space with norm defined by: ‖(xn)‖ = ‖(‖xn‖)‖E. This type of space has long been the source of examples and counter-examples in the geometric theory of Banach spaces. For instance, Day [7] used E=lp and Xk=lqk, with appropriate choice of qk, to give an example of a reflexive Banach space not isomorphic to any uniformly conves Banach space. Recently VanDulst and Devalk [33] have considered Orlicz sums of Banach spaces in their studies of Kadec-Klee property.

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12

Coleman, E. "Banach Space Ultraproducts." Irish Mathematical Society Bulletin 0018 (1987): 30–39. http://dx.doi.org/10.33232/bims.0018.30.39.

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13

Cho, Ilwoo. "p-adic Banach space operators and adelic Banach space operators." Opuscula Mathematica 34, no. 1 (2014): 29. http://dx.doi.org/10.7494/opmath.2014.34.1.29.

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14

Shang, Shaoqiang, and Yunan Cui. "Approximative Compactness and Radon-Nikodym Property inw∗Nearly Dentable Banach Spaces and Applications." Journal of Function Spaces 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/921456.

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Authors definew∗nearly dentable Banach space. Authors study Radon-Nikodym property, approximative compactness and continuity metric projector operator inw∗nearly dentable space. Moreover, authors obtain some examples ofw∗nearly dentable space in Orlicz function spaces. Finally, by the method of geometry of Banach spaces, authors give important applications ofw∗nearly dentability in generalized inverse theory of Banach space.

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15

Castillo, J. M. F., and M. A. Simoes. "On the three-space problem for the Dunford-Pettis property." Bulletin of the Australian Mathematical Society 60, no. 3 (December 1999): 487–93. http://dx.doi.org/10.1017/s0004972700036650.

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A Banach space X is called a twisted sum of the Banach spaces Y and Z if it has a subspace isomorphic to Y in such a way that the corresponding quotient is isomorphic to Z. In this paper we study twisted sums of Banach spaces with either have the Dunford-Pettis property, are c0-saturated or l1-saturated. Amongst other things, we show that every Banach space is a complemented subspace of a twisted sum of two Banach spaces with the Dunford-Pettis property.

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16

Barnes, Benedict, I. A. Adjei, S. K. Amponsah, and E. Harris. "Product-Normed Linear Spaces." European Journal of Pure and Applied Mathematics 11, no. 3 (July 31, 2018): 740–50. http://dx.doi.org/10.29020/nybg.ejpam.v11i3.3284.

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In this paper, both the product-normed linear space $P-NLS$ (product-Banach space) and product-semi-normed linear space (product-semi-Banch space) are introduced. These normed linear spaces are endowed with the first and second product inequalities, which have a lot of applications in linear algebra and differential equations. In addition, we showed that $P-NLS$ admits functional properties such as completeness, continuity and the fixed point.

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17

JAIN, P. K., S. K. KAUSHIK, and NISHA GUPTA. "ON FRAME SYSTEMS IN BANACH SPACES." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 01 (January 2009): 1–7. http://dx.doi.org/10.1142/s021969130900274x.

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Banach frame systems in Banach spaces have been defined and studied. A sufficient condition under which a Banach space, having a Banach frame, has a Banach frame system has been given. Also, it has been proved that a Banach space E is separable if and only if E* has a Banach frame ({φn},T) with each φn weak*-continuous. Finally, a necessary and sufficient condition for a Banach Bessel sequence to be a Banach frame has been given.

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18

Osipov, Alexander. "Note on the Banach problem 1 of condensations of Banach spaces onto compacta." Filomat 37, no. 7 (2023): 2183–86. http://dx.doi.org/10.2298/fil2307183o.

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It is consistent with any possible value of the continuum c that every infinite-dimensional Banach space of density ? c condenses onto the Hilbert cube. Let ? < c be a cardinal of uncountable cofinality. It is consistent that the continuum be arbitrary large, no Banach space X of density ?, ? < ? < c, condenses onto a compact metric space, but any Banach space of density ? admits a condensation onto a compact metric space. In particular, for ? = ?1, it is consistent that c is arbitrarily large, no Banach space of density ?, ?1 < ? < c, condenses onto a compact metric space. These results imply a complete answer to the Problem 1 in the Scottish Book for Banach spaces: When does a Banach space X admit a bijective continuous mapping onto a comact metric space?

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19

SHARMA, SHALU. "ON BI-BANACH FRAMES IN BANACH SPACES." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 02 (March 2014): 1450015. http://dx.doi.org/10.1142/s0219691314500155.

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Bi-Banach frames in Banach spaces have been defined and studied. A necessary and sufficient condition under which a Banach space has a Bi-Banach frame has been given. Finally, Pseudo exact retro Banach frames have been defined and studied.

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20

Heinrich, S., C. Ward Henson, and L. C. Moore. "A note on elementary equivalence of C(K) spaces." Journal of Symbolic Logic 52, no. 2 (June 1987): 368–73. http://dx.doi.org/10.2307/2274386.

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In this paper we give a closer analysis of the elementary properties of the Banach spaces C(K), where K is a totally disconnected, compact Hausdorff space, in terms of the Boolean algebra B(K) of clopen subsets of K. In particular we sharpen a result in [4] by showing that if B(K1) and B(K2) satisfy the same sentences with ≤ n alternations of quantifiers, then the same is true of C(K1) and C(K2). As a consequence we show that for each n there exist C(K) spaces which are elementarily equivalent for sentences with ≤ n quantifier alternations, but which are not elementary equivalent in the full sense. Thus the elementary properties of Banach spaces cannot be determined by looking at sentences with a bounded number of quantifier alternations.The notion of elementary equivalence for Banach spaces which is studied here was introduced by the second author [4] and is expressed using the language of positive bounded formulas in a first-order language for Banach spaces. As was shown in [4], two Banach spaces are elementarily equivalent in this sense if and only if they have isometrically isomorphic Banach space ultrapowers (or, equivalently, isometrically isomorphic nonstandard hulls.)We consider Banach spaces over the field of real numbers. If X is such a space, Bx will denote the closed unit ball of X, Bx = {x ϵ X∣ ∣∣x∣∣ ≤ 1}. Given a compact Hausdorff space K, we let C(K) denote the Banach space of all continuous real-valued functions on K, under the supremum norm. We will especially be concerned with such spaces when K is a totally disconnected compact Hausdorff space. In that case B(K) will denote the Boolean algebra of all clopen subsets of K. We adopt the standard notation from model theory and Banach space theory.

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González, Manuel, and Joaquín M. Gutiérrez. "The compact weak topology on a Banach space." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 120, no. 3-4 (1992): 367–79. http://dx.doi.org/10.1017/s0308210500032194.

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SynopsisThe compact weak topology (kw) on a Banach space is defined as the finest topology that agrees with the weak topology on weakly compact subsets. It appears in a natural manner in the study of certain classes of continuous and holomorphic maps between Banach spaces. In this paper we treat the kw topology and the finest locally convex topology contained in kw, which we call the ckw topology. We prove that kw = ckw if and only if the space is reflexive or Schur, and we derive characterisations of Banach spaces not containing l1, and of other classes of Banach spaces, in terms of these topologies. We also show that ckw is the topology of uniform convergence on (L)-subsets of the dual space. As a consequence, Banach spaces with the reciprocal Dunford–Pettis property are characterised.

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ARENDT, W., I. CHALENDAR, M. KUMAR, and S. SRIVASTAVA. "POWERS OF COMPOSITION OPERATORS: ASYMPTOTIC BEHAVIOUR ON BERGMAN, DIRICHLET AND BLOCH SPACES." Journal of the Australian Mathematical Society 108, no. 3 (November 27, 2019): 289–320. http://dx.doi.org/10.1017/s1446788719000235.

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We study the asymptotic behaviour of the powers of a composition operator on various Banach spaces of holomorphic functions on the disc, namely, standard weighted Bergman spaces (finite and infinite order), Bloch space, little Bloch space, Bloch-type space and Dirichlet space. Moreover, we give a complete characterization of those composition operators that are similar to an isometry on these various Banach spaces. We conclude by studying the asymptotic behaviour of semigroups of composition operators on these various Banach spaces.

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Jiménez-Melado, A. "Stability of weak normal structure in James quasi reflexive space." Bulletin of the Australian Mathematical Society 46, no. 3 (December 1992): 367–72. http://dx.doi.org/10.1017/s0004972700012016.

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We introduce a coefficient on general Banach spaces which allows us to derive the weak normal structure for those Banach spaces whose Banach-Mazur distance to James quasi reflexive space is less than .

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Tian, Lixin, Jiangbo Zhou, Xun Liu, and Guangsheng Zhong. "Nonwandering operators in Banach space." International Journal of Mathematics and Mathematical Sciences 2005, no. 24 (2005): 3895–908. http://dx.doi.org/10.1155/ijmms.2005.3895.

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We introduce nonwandering operators in infinite-dimensional separable Banach space. They are new linear chaotic operators and are relative to hypercylic operators, but different from them. Firstly, we show some examples for nonwandering operators in some typical infinite-dimensional Banach spaces, including Banach sequence space and physical background space. Then we present some properties of nonwandering operators and the spectra decomposition of invertible nonwandering operators. Finally, we obtain that invertible nonwandering operators are locally structurally stable.

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25

Laustsen, Niels Jakob. "MAXIMAL IDEALS IN THE ALGEBRA OF OPERATORS ON CERTAIN BANACH SPACES." Proceedings of the Edinburgh Mathematical Society 45, no. 3 (October 2002): 523–46. http://dx.doi.org/10.1017/s0013091500001097.

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AbstractFor a Banach space $\mathfrak{X}$, let $\mathcal{B}(\mathfrak{X})$ denote the Banach algebra of all continuous linear operators on $\mathfrak{X}$. First, we study the lattice of closed ideals in $\mathcal{B}(\mathfrak{J}_p)$, where $1 \lt p \t \infty$ and $\mathfrak{J}_p$ is the $p$th James space. Our main result is that the ideal of weakly compact operators is the unique maximal ideal in $\mathcal{B}(\mathfrak{J}_p)$. Applications of this result include the following.(i) The Brown–McCoy radical of $\mathcal{B}(\mathfrak{X})$, which by definition is the intersection of all maximal ideals in $\mathcal{B}(\mathfrak{X})$, cannot be turned into an operator ideal. This implies that there is no ‘Brown–McCoy’ analogue of Pietsch’s construction of the operator ideal of inessential operators from the Jacobson radical of $\mathcal{B}(\mathfrak{X})/\mathcal{A}(\mathfrak{X})$.(ii) For each natural number $n$ and each $n$-tuple $(m_1,\dots,m_n)$ in $\{k^2\mid k\in\mathbb{N}\}\cup\{\infty\}$, there is a Banach space $\mathfrak{X}$ such that $\mathcal{B}(\mathfrak{X})$ has exactly $n$ maximal ideals, and these maximal ideals have codimensions $m_1,\dots,m_n$ in $\mathcal{B}(\mathfrak{X})$, respectively; the Banach space $\mathfrak{X}$ is a finite direct sum of James spaces and $\ell_p$-spaces.Second, building on the work of Gowers and Maurey, we obtain further examples of Banach spaces $\mathfrak{X}$ such that all the maximal ideals in $\mathcal{B}(\mathfrak{X})$ can be classified. We show that the ideal of strictly singular operators is the unique maximal ideal in $\mathcal{B}(\mathfrak{X})$ for each hereditarily indecomposable Banach space $\mathfrak{X}$, and we prove that there are $2^{2^{\aleph_0}}$ distinct maximal ideals in $\mathcal{B}(\mathfrak{G})$, where $\mathfrak{G}$ is the Banach space constructed by Gowers to solve Banach’s hyperplane problem.AMS 2000 Mathematics subject classification: Primary 47D30; 47D50; 46H10; 16D30

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Leiderman, Arkady, and Sidney Morris. "Separability of Topological Groups: A Survey with Open Problems." Axioms 8, no. 1 (December 29, 2018): 3. http://dx.doi.org/10.3390/axioms8010003.

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Separability is one of the basic topological properties. Most classical topological groups and Banach spaces are separable; as examples we mention compact metric groups, matrix groups, connected (finite-dimensional) Lie groups; and the Banach spaces C ( K ) for metrizable compact spaces K; and ℓ p , for p ≥ 1 . This survey focuses on the wealth of results that have appeared in recent years about separable topological groups. In this paper, the property of separability of topological groups is examined in the context of taking subgroups, finite or infinite products, and quotient homomorphisms. The open problem of Banach and Mazur, known as the Separable Quotient Problem for Banach spaces, asks whether every Banach space has a quotient space which is a separable Banach space. This paper records substantial results on the analogous problem for topological groups. Twenty open problems are included in the survey.

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Chō, Muneo, Injo Hur, and Ji Lee. "Numerical ranges of conjugations and antilinear operators on a Banach space." Filomat 35, no. 8 (2021): 2715–20. http://dx.doi.org/10.2298/fil2108715c.

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In this paper, we prove that the numerical range of a conjugation on Banach spaces, using the connected property, is either the unit circle or the unit disc depending the dimension of the given Banach space. When a Banach space is reflexive, we have the same result for the numerical range of a conjugation by applying path-connectedness which is applicable to the Hilbert space setting. In addition, we show that the numerical ranges of antilinear operators on Banach spaces are contained in annuli.

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Castillo, Jesús M. F., and Fernando Sánchez. "Upper lp-estimates in vector sequence spaces, with some applications." Mathematical Proceedings of the Cambridge Philosophical Society 113, no. 2 (March 1993): 329–34. http://dx.doi.org/10.1017/s030500410007599x.

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In [11], Partington proved that if λ is a Banach sequence space with a monotone basis having the Banach-Saks property, and (Xn) is a sequence of Banach spaces each having the Banach-Saks property, then the vector sequence space ΣλXn has this same property. In addition, Partington gave an example showing that if λ and each Xn, have the weak Banach-Saks property, then ΣλXn need not have the weak Banach-Saks property.

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Sid Ahmed, Ould Ahmed Mahmoud. "m-ISOMETRIC OPERATORS ON BANACH SPACES." Asian-European Journal of Mathematics 03, no. 01 (March 2010): 1–19. http://dx.doi.org/10.1142/s1793557110000027.

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We introduce the class of m-isometric operators on Banach spaces. This generalizes to Banach space the m-isometric operators on Hilbert space introduced by Agler and Stankus. We establish some basic properties and we introduce the notion of m-invertibility as a natural generalization of the invertibility on Banach spaces.

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30

Koszmider, Piotr, Miguel Martín, and Javier Merí. "Isometries on extremely non-complex Banach spaces." Journal of the Institute of Mathematics of Jussieu 10, no. 2 (July 14, 2010): 325–48. http://dx.doi.org/10.1017/s1474748010000204.

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AbstractGiven a separable Banach space E, we construct an extremely non-complex Banach space (i.e. a space satisfying that ‖ Id + T2 ‖ = 1 + ‖ T2 ‖ for every bounded linear operator T on it) whose dual contains E* as an L-summand. We also study surjective isometries on extremely non-complex Banach spaces and construct an example of a real Banach space whose group of surjective isometries reduces to ±Id, but the group of surjective isometries of its dual contains the group of isometries of a separable infinite-dimensional Hilbert space as a subgroup.

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Abrahamsen, Trond, Vegard Lima, André Martiny, and Stanimir Troyanski. "Daugavet- and delta-points in Banach spaces with unconditional bases." Transactions of the American Mathematical Society, Series B 8, no. 13 (April 28, 2021): 379–98. http://dx.doi.org/10.1090/btran/68.

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We study the existence of Daugavet- and delta-points in the unit sphere of Banach spaces with a 1 1 -unconditional basis. A norm one element x x in a Banach space is a Daugavet-point (resp. delta-point) if every element in the unit ball (resp. x x itself) is in the closed convex hull of unit ball elements that are almost at distance 2 2 from x x . A Banach space has the Daugavet property (resp. diametral local diameter two property) if and only if every norm one element is a Daugavet-point (resp. delta-point). It is well-known that a Banach space with the Daugavet property does not have an unconditional basis. Similarly spaces with the diametral local diameter two property do not have an unconditional basis with suppression unconditional constant strictly less than 2 2 . We show that no Banach space with a subsymmetric basis can have delta-points. In contrast we construct a Banach space with a 1 1 -unconditional basis with delta-points, but with no Daugavet-points, and a Banach space with a 1 1 -unconditional basis with a unit ball in which the Daugavet-points are weakly dense.

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32

Labuschagne, C. C. A. "Preduals and Nuclear Operators Associated with Bounded, p-Convex, p-Concave and Positive p-Summing Operators." Canadian Journal of Mathematics 59, no. 3 (June 1, 2007): 614–37. http://dx.doi.org/10.4153/cjm-2007-026-2.

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AbstractWe use Krivine's form of the Grothendieck inequality to renorm the space of bounded linear maps acting between Banach lattices. We construct preduals and describe the nuclear operators associated with these preduals for this renormed space of bounded operators as well as for the spaces of p-convex, p-concave and positive p-summing operators acting between Banach lattices and Banach spaces. The nuclear operators obtained are described in terms of factorizations through classical Banach spaces via positive operators.

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33

Bombal, Fernando. "On l1 subspaces of Orlicz vector-valued function spaces." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 1 (January 1987): 107–12. http://dx.doi.org/10.1017/s0305004100066445.

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The purpose of this paper is to characterize the Orlicz vector-valued function spaces containing a copy or a complemented copy of l1. Pisier proved in [13] that if a Banach space E contains no copy of l1, then the space Lp(S, Σ, μ, E) does not contain it either, for 1 < p < ∞. We extend this result to the case of Orlicz vector valued function spaces, by reducing the problem to the situation considered by Pisier. Next, we pass to study the problem of embedding l1 as a complemented subspace of LΦ(E). We obtain a complete characterization when E is a Banach lattice and only partial results in case of a general Banach space. We use here in a crucial way a result of E. Saab and P. Saab concerning the embedding of l1 as a complemented subspace of C(K, E), the Banach space of all the E-valued continuous functions on the compact Hausdorff space K (see [14]). Finally, we use these results to characterize several classes of Banach spaces for which LΦ(E) has some Banach space properties, namely the reciprocal Dunford-Pettis property and Pelczyński's V property.

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34

Rauhut, Holger. "Coorbit space theory for quasi-Banach spaces." Studia Mathematica 180, no. 3 (2007): 237–53. http://dx.doi.org/10.4064/sm180-3-4.

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35

González, Manuel, and Antonio Martínez-Abejón. "Local dual spaces of a Banach space." Studia Mathematica 147, no. 2 (2001): 155–68. http://dx.doi.org/10.4064/sm147-2-4.

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36

Deng, Chunyan, and M. S. Balasubramani. "Submaximal operator space structures on Banach spaces." Operators and Matrices, no. 3 (2013): 723–32. http://dx.doi.org/10.7153/oam-07-40.

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37

Rehman, Saif Ur, Arjamand Bano, Hassen Aydi, and Choonkil Park. "An approach of Banach algebra in fuzzy metric spaces with an application." AIMS Mathematics 7, no. 5 (2022): 9493–507. http://dx.doi.org/10.3934/math.2022527.

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<abstract><p>The purpose of this paper is to present a new concept of a Banach algebra in a fuzzy metric space (FM-space). We define an open ball, an open set and prove that every open ball in an FM-space over a Banach algebra $ \mathcal{A} $ is an open set. We present some more topological properties and a Hausdorff metric on FM-spaces over $ \mathcal{A} $. Moreover, we state and prove a fuzzy Banach contraction theorem on FM-spaces over a Banach algebra $ \mathcal{A} $. Furthermore, we present an application of an integral equation and will prove a result dealing with the integral operators in FM-spaces over a Banach algebra.</p></abstract>

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38

Josefson, Bengt. "A Gelfand-Phillips space not containing l1 whose dual ball is not weak * sequentially compact." Glasgow Mathematical Journal 43, no. 1 (January 2001): 125–28. http://dx.doi.org/10.1017/s0017089501010114.

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A set D in a Banach space E is called limited if pointwise convergent sequences of linear functionals converge uniformly on D and E is called a GP-space (after Gelfand and Phillips) if every limited set in E is relatively compact. Banach spaces with weak * sequentially compact dual balls (W*SCDB for short) are GP-spaces and l1 is a GP-space without W*SCDB. Disproving a conjecture of Rosenthal and inspired by James tree space, Hagler and Odell constructed a class of Banach spaces ([HO]-spaces) without both W*SCDB and subspaces isomorphic to l1. Schlumprecht has shown that there is a subclass of the [HO]-spaces which are also GP-spaces. It is not clear however if any [HO]-construction yields a GP-space—in fact it is not even clear that W*SCDB[lrarr ]GP-space is false in general for the class of Banach spaces containing no subspace isomorphic to l1. In this note the example of Hagler and Odell is modified to yield a GP-space without W*SCDB and without an isomorphic copy of l1.

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39

Banakh, Taras, and Joanna Garbulińska-Wȩgrzyn. "Universal decomposed Banach spaces." Banach Journal of Mathematical Analysis 14, no. 2 (January 1, 2020): 470–86. http://dx.doi.org/10.1007/s43037-019-00003-7.

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AbstractLet $${\mathcal {B}}$$B be a class of finite-dimensional Banach spaces. A $${\mathcal {B}}$$B-decomposed Banach space is a Banach space X endowed with a family $${\mathcal {B}}_X\subset {\mathcal {B}}$$BX⊂B of subspaces of X such that each $$x\in X$$x∈X can be uniquely written as the sum of an unconditionally convergent series $$\sum _{B\in {\mathcal {B}}_X}x_B$$∑B∈BXxB for some $$(x_B)_{B\in {\mathcal {B}}_X}\in \prod _{B\in {\mathcal {B}}_X}B$$(xB)B∈BX∈∏B∈BXB. For every $$B\in {\mathcal {B}}_X$$B∈BX let $$\mathrm {pr}_B:X\rightarrow B$$prB:X→B denote the coordinate projection. Let $$C\subset [-1,1]$$C⊂[-1,1] be a closed convex set with $$C\cdot C\subset C$$C·C⊂C. The C-decomposition constant $$K_C$$KC of a $${\mathcal {B}}$$B-decomposed Banach space $$(X,{\mathcal {B}}_X)$$(X,BX) is the smallest number $$K_C$$KC such that for every function $$\alpha :{\mathcal {F}}\rightarrow C$$α:F→C from a finite subset $${\mathcal {F}}\subset {\mathcal {B}}_X$$F⊂BX the operator $$T_\alpha =\sum _{B\in {\mathcal {F}}}\alpha (B)\cdot \mathrm {pr}_B$$Tα=∑B∈Fα(B)·prB has norm $$\Vert T_\alpha \Vert \le K_C$$‖Tα‖≤KC. By $$\varvec{{\mathcal {B}}}_C$$BC we denote the class of $${\mathcal {B}}$$B-decomposed Banach spaces with C-decomposition constant $$K_C\le 1$$KC≤1. Using the technique of Fraïssé theory, we construct a rational $${\mathcal {B}}$$B-decomposed Banach space $$\mathbb {U}_C\in \varvec{{\mathcal {B}}}_C$$UC∈BC which contains an almost isometric copy of each $${\mathcal {B}}$$B-decomposed Banach space $$X\in \varvec{{\mathcal {B}}}_C$$X∈BC. If $${\mathcal {B}}$$B is the class of all 1-dimensional (resp. finite-dimensional) Banach spaces, then $$\mathbb {U}_{C}$$UC is isomorphic to the complementably universal Banach space for the class of Banach spaces with an unconditional (f.d.) basis, constructed by Pełczyński (and Wojtaszczyk).

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40

Öztop, Serap. "Multipliers of Banach valued weighted function spaces." International Journal of Mathematics and Mathematical Sciences 24, no. 8 (2000): 511–17. http://dx.doi.org/10.1155/s0161171200004361.

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We generalize Banach valued spaces to Banach valued weighted function spaces and study the multipliers space of these spaces. We also show the relationship between multipliers and tensor product of Banach valued weighted function spaces.

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41

Xu, Hong-Kun. "Strong Convergence of Approximating Fixed Point Sequences for Nonexpansive Mappings." Bulletin of the Australian Mathematical Society 74, no. 1 (January 2006): 143–51. http://dx.doi.org/10.1017/s0004972700047535.

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Consider a nonexpansive self-mapping T of a bounded closed convex subset of a Banach space. Banach's contraction principle guarantees the existence of approximating fixed point sequences for T. However such sequences may not be strongly convergent, in general, even in a Hilbert space. It is shown in this paper that in a real smooth and uniformly convex Banach space, appropriately constructed approximating fixed point sequences can be strongly convergent.

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42

Effros, Edward G., and Zhong-Jin Ruan. "A New Approach to Operator Spaces." Canadian Mathematical Bulletin 34, no. 3 (September 1, 1991): 329–37. http://dx.doi.org/10.4153/cmb-1991-053-x.

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AbstractThe authors previously observed that the space of completely bounded maps between two operator spaces can be realized as an operator space. In particular, with the appropriate matricial norms the dual of an operator space V is completely isometric to a linear space of operators. This approach to duality enables one to formulate new analogues of Banach space concepts and results. In particular, there is an operator space version ⊗μ of the Banach space projective tensor product , which satisfies the expected functorial properties. As is the case for Banach spaces, given an operator space V, the functor W |—> V ⊗μ W preserves inclusions if and only if is an injective operator space.

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43

Cima, Joseph A., and Michael Stessin. "On the Recovery of Analytic Functions." Canadian Journal of Mathematics 48, no. 2 (April 1, 1996): 288–301. http://dx.doi.org/10.4153/cjm-1996-015-4.

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AbstractIn this paper we consider questions of recapturing an analytic function in a Banach space from its values on a uniqueness set. The principal method is to use reproducing kernels to construct a sequence in the Banach space which converges in norm to the given functions. The method works for several classical Banach spaces of analytic functions including some Hardy and Bergman spaces.

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44

AIZPURU, ANTONIO, and FRANCISCO J. GARCÍA-PACHECO. "A NOTE ON L2-SUMMAND VECTORS IN DUAL SPACES." Glasgow Mathematical Journal 50, no. 3 (September 2008): 429–32. http://dx.doi.org/10.1017/s0017089508004308.

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AbstractIt is shown that every L2-summand vector of a dual real Banach space is a norm-attaining functional. As consequences, the L2-summand vectors of a dual real Banach space can be determined by the L2-summand vectors of its predual; for every n ∈ , every real Banach space can be equivalently renormed so that the set of norm-attaining functionals is n-lineable; and it is easy to find equivalent norms on non-reflexive dual real Banach spaces that are not dual norms.

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45

Fourie, J. H. "Absoluut sommerende vermenigvuldigers en die Dvoretzky-Rogers - stelling." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 9, no. 2 (July 5, 1990): 73–76. http://dx.doi.org/10.4102/satnt.v9i2.453.

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The space M(E) of absolutely summing multipliers of a Banach space E is considered. For some special types of Banach spaces E it turns out that M (E) can he characterized as an lᴾ-space of absolutely summable scalar sequences. We provide some important examples of Banach spaces for which the lᴾ-characterizations of M(E) hold true. The well known Dvoretzky-Rogers theorem plays an important role in these characterizations. An “alternative" version of the last mentioned theorem is discussed.

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46

Fonf, Vladimir P., and Clemente Zanco. "Covering a Banach space." Proceedings of the American Mathematical Society 134, no. 9 (February 17, 2006): 2607–11. http://dx.doi.org/10.1090/s0002-9939-06-08254-2.

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47

Westwood, Derek J. "Nests in Banach space." Journal of Mathematical Analysis and Applications 156, no. 2 (April 1991): 558–67. http://dx.doi.org/10.1016/0022-247x(91)90414-u.

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48

Kim, Sung Guen, and Han Ju Lee. "Generalized Numerical Index and Denseness of Numerical Peak Holomorphic Functions on a Banach Space." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/380475.

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The generalized numerical index of a Banach space is introduced, and its properties on certain Banach spaces are studied. Ed-dari's theorem on the numerical index is extended to the generalized index and polynomial numerical index of a Banach space. The denseness of numerical strong peak holomorphic functions is also studied.

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49

Zachariades, Theodosis. "Weakly stable Banach spaces and the Banach-Saks properties." Glasgow Mathematical Journal 35, no. 1 (January 1993): 79–83. http://dx.doi.org/10.1017/s0017089500009587.

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In [9] J. L. Krivine and B. Maurey introduced the class of stable Banach spaces: a separable Banach space is called stable if for every pair of bounded sequences (xn)n, (yn)n and for every pair of ultrafilters on the natural numbers we have

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Aljuaid, Munirah, and Flavia Colonna. "Composition Operators on Some Banach Spaces of Harmonic Mappings." Journal of Function Spaces 2020 (February 19, 2020): 1–11. http://dx.doi.org/10.1155/2020/9034387.

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We study the composition operators on Banach spaces of harmonic mappings that extend several well-known Banach spaces of analytic functions on the open unit disk in the complex plane, including the α-Bloch spaces, the growth spaces, the Zygmund space, the analytic Besov spaces, and the space BMOA.

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