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Journal articles on the topic 'Banach space'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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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 (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

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5

Mohi, Hala Majed, Enas Ajil Jasim, and Aya Adnan Mousa Abd. "Analysis of applications of Banach fixed point theorem." Experimental and Theoretical NANOTECHNOLOGY 9, S (2025): 115–22. https://doi.org/10.56053/9.s.115.

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In the context of normed space, Banach's fixed point theorem for mapping is studied in this paper. This idea is generalized in Banach's classical fixed-point theory. Fixed point theory explains many situations where maps provide great answers through an amazing combination of mathematical analysis. Picard- Lendell's theorem, Picard's theorem, implicit function theorem, and other results are created by other mathematicians later using this fixed-point theorem. We have come up with ideas that Banach's theorem can be used to easily deduce many well-known fixed-point theorems. Extending the Banach

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6

Ghosh, P., та T. K. Samanta. "Об устойчивости ретро банахова фрейма относительно b-линейного функционала в n-банаховом пространстве". Владикавказский математический журнал, № 1 (23 березня 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 respec

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7

Morris, Sidney A., and David T. Yost. "Observations on the Separable Quotient Problem for Banach Spaces." Axioms 9, no. 1 (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 precisel

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8

Kusraev, Anatoly, and Semën Kutateladze. "Geometric Characterization of Injective Banach Lattices." Mathematics 9, no. 3 (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

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9

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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10

Ajay Kumar Chaudhary. "Extension and Generalization of Banach Contraction in Metric and in Menger Space." Communications on Applied Nonlinear Analysis 32, no. 2 (2024): 53–63. http://dx.doi.org/10.52783/cana.v32.1707.

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The root of metric fixed point theory is Stefen Banach's contraction mapping, a research source for shrinking the distance between two points in space. As a source, many authors have introduced many contraction mappings as extensions and generalizations of Banach contraction and established fixed point theorems under the property that each such mapping in complete metric and Menger space has a unique fixed point. This article presents updated results of Banach contraction generalization and extension forms in metric and Menger space which helps the comparative and interrelationship study in th

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11

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 (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-dime

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12

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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13

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 (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 space

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14

Dixmier, Jacques. "Operateurs hypofermes." Journal of Operator Theory 91, no. 2 (2024): 323–33. https://doi.org/10.7900/jot.2023nov13.2451.

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Range spaces of bounded linear operators between Hilbert spaces, as well as linear operators between Hilbert spaces, whose graph is a bounded linear range of some Hilbert space, were systematically studied in an early paper. Here extensions of the above topics to the framework of general Banach spaces are discussed. A hypoclosed linear subspace of a Banach space is the range space of a bounded linear operator defined on some Banach space, while a hypoclosed linear operator is a linear operator between Banach spaces, whose graph is hypoclosed. Characterizations, permanence properties, pathologi

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15

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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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 (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

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. Thes

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18

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 (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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19

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 (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 s

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20

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 (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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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 (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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22

Laustsen, Niels Jakob. "MAXIMAL IDEALS IN THE ALGEBRA OF OPERATORS ON CERTAIN BANACH SPACES." Proceedings of the Edinburgh Mathematical Society 45, no. 3 (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 idea

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23

Leiderman, Arkady, and Sidney Morris. "Separability of Topological Groups: A Survey with Open Problems." Axioms 8, no. 1 (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.

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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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25

SHARMA, SHALU. "ON BI-BANACH FRAMES IN BANACH SPACES." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 02 (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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26

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 (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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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 (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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Sid Ahmed, Ould Ahmed Mahmoud. "m-ISOMETRIC OPERATORS ON BANACH SPACES." Asian-European Journal of Mathematics 03, no. 01 (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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29

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 top

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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 (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 unc

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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 (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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Bombal, Fernando. "On l1 subspaces of Orlicz vector-valued function spaces." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 1 (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

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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 (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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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 integra

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35

BERINDE, VASILE. "Existence and approximation of fixed points of enriched contractions in quasi-Banach spaces." Carpathian Journal of Mathematics 40, no. 2 (2024): 263–74. http://dx.doi.org/10.37193/cjm.2024.02.03.

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We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the previous results for enriched contractions defined on Banach spaces [Berinde, V.; P˘acurar, M. Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 38, 10 pp.]. The theoretical results are illustrated by means of an appropriate example of enriched contraction on a quasi-Banach space which is not a Banach space and thus show that our new results are effective generalizations of the previo

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36

Josefson, Bengt. "A Gelfand-Phillips space not containing l1 whose dual ball is not weak * sequentially compact." Glasgow Mathematical Journal 43, no. 1 (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

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37

Xu, Hong-Kun. "Strong Convergence of Approximating Fixed Point Sequences for Nonexpansive Mappings." Bulletin of the Australian Mathematical Society 74, no. 1 (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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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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39

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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40

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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41

O.P, Gupta* &. Madhuri .Shrama. "FIXED POINT THEOREMS IN BANACH SPACE AND 2-BANACH SPACE." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES [FRTSSDS- June 2018] (June 20, 2018): 137–43. https://doi.org/10.5281/zenodo.1293831.

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We generalize the result of Goebel and Zlotkiewiez [5] and also we prove fixed point theorems in Banach and 2-Banach spaces in this paper.   <strong>Subject Classification (AMS 2000)  :</strong>  47H10, 54H25

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42

Effros, Edward G., and Zhong-Jin Ruan. "A New Approach to Operator Spaces." Canadian Mathematical Bulletin 34, no. 3 (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

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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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44

Cima, Joseph A., and Michael Stessin. "On the Recovery of Analytic Functions." Canadian Journal of Mathematics 48, no. 2 (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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45

AIZPURU, ANTONIO, and FRANCISCO J. GARCÍA-PACHECO. "A NOTE ON L2-SUMMAND VECTORS IN DUAL SPACES." Glasgow Mathematical Journal 50, no. 3 (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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46

Fourie, J. H. "Absoluut sommerende vermenigvuldigers en die Dvoretzky-Rogers - stelling." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 9, no. 2 (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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Dutta, Hemen, B. V. Senthil Kumar, and S. Sabarinathan. "Fuzzy stabilities of a new hexic functional equation in various spaces." Analele Universitatii "Ovidius" Constanta - Seria Matematica 30, no. 3 (2022): 143–71. https://doi.org/10.2478/auom-2022-0038.

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Abstract The advantage of various fuzzy normed spaces is to analyse impreciseness and ambiguity that arise in modelling problems. In this paper, various classical stabilities of a new hexic functional equation in di erent fuzzy spaces like fuzzy Banach space, Felbin’s fuzzy Banach space and intuitionistic fuzzy Banach space are presented, concerning the Ulam’s theory of stabilities of equations. To validate the stability results, experimental results are presented. Also, a comparative study of the results obtained in this investigation are provided.

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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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Savitha. S. "Theorems for Near Stable Points on a Near Banach Space Furnished with Graph." Communications on Applied Nonlinear Analysis 31, no. 2 (2024): 156–73. http://dx.doi.org/10.52783/cana.v31.527.

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The paper introduces a novel method for defining the graph associated with a near Banach space. In mathematics, a graph typically represents relationships between objects. Here, it seems the graph is being defined in the context of a near Banach space, which is a generalization of Banach spaces allowing the norm to take infinite values. An iteration function is utilized to define the subgraph of the graph associated with the near Banach space. This subgraph likely captures specific properties or relationships within the original graph. The paper presents near-fixed point theorems by well-known

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Banakh, Taras, and Joanna Garbulińska-Wȩgrzyn. "Universal decomposed Banach spaces." Banach Journal of Mathematical Analysis 14, no. 2 (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 $$

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