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Journal articles on the topic 'Geometry of Banach spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Muñoz-Fernández, Gustavo A., and Juan B. Seoane-Sepúlveda. "Geometry of Banach spaces of trinomials." Journal of Mathematical Analysis and Applications 340, no. 2 (April 2008): 1069–87. http://dx.doi.org/10.1016/j.jmaa.2007.09.010.

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2

Okeke, Godwin Amechi, and Mujahid Abbas. "Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces." Applied General Topology 21, no. 1 (April 3, 2020): 135. http://dx.doi.org/10.4995/agt.2020.12220.

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It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

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3

Lee, Han Ju. "RANDOMIZED SERIES AND GEOMETRY OF BANACH SPACES." Taiwanese Journal of Mathematics 14, no. 5 (October 2010): 1837–48. http://dx.doi.org/10.11650/twjm/1500406019.

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4

TASKINEN, JARI. "Inductive limits and geometry of Banach spaces." Mathematical Proceedings of the Cambridge Philosophical Society 126, no. 1 (January 1999): 99–107. http://dx.doi.org/10.1017/s0305004198003077.

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5

Pietsch, A. "Eigenvalue Distributions and Geometry of Banach Spaces." Mathematische Nachrichten 150, no. 1 (1991): 41–81. http://dx.doi.org/10.1002/mana.19911500105.

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6

Becerra Guerrero, Julio, and Angel Rodriguez Palacios. "The Geometry of Convex Transitive Banach Spaces." Bulletin of the London Mathematical Society 31, no. 3 (May 1999): 323–31. http://dx.doi.org/10.1112/s0024609398005359.

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7

Granero, A. S., M. Jiménez Sevilla, and J. P. Moreno. "Geometry of Banach spaces with property β." Israel Journal of Mathematics 111, no. 1 (December 1999): 263–73. http://dx.doi.org/10.1007/bf02810687.

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8

Alber, Y. I., R. S. Burachik, and A. N. Iusem. "A proximal point method for nonsmooth convex optimization problems in Banach spaces." Abstract and Applied Analysis 2, no. 1-2 (1997): 97–120. http://dx.doi.org/10.1155/s1085337597000298.

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In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.

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9

Garrido, M. Isabel, Jesús A. Jaramillo, and José G. Llavona. "Polynomial topologies on Banach spaces." Topology and its Applications 153, no. 5-6 (December 2005): 854–67. http://dx.doi.org/10.1016/j.topol.2005.01.015.

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10

Adams, Tarn. "Flat Chains in Banach Spaces." Journal of Geometric Analysis 18, no. 1 (December 7, 2007): 1–28. http://dx.doi.org/10.1007/s12220-007-9008-5.

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11

Albiac, Fernando, and Camino Leránoz. "Drops in Quasi-Banach Spaces." Journal of Geometric Analysis 20, no. 3 (March 23, 2010): 525–37. http://dx.doi.org/10.1007/s12220-010-9118-3.

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12

Khalil, R., D. Hussein, and W. Amin. "Geometry of Modulus Spaces." gmj 9, no. 2 (June 2002): 295–301. http://dx.doi.org/10.1515/gmj.2002.295.

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Abstract Let ϕ be a modulus function, i.e., continuous strictly increasing function on [0, ∞), such that ϕ(0) = 0, ϕ(1) = 1, and ϕ(𝑥+𝑦) ≤ ϕ(𝑥)+ϕ(𝑦) for all 𝑥, 𝑦 in [0, ∞). It is the object of this paper to characterize, for any Banach space 𝑋, extreme points, exposed points, and smooth points of the unit ball of the metric linear space ℓ ϕ (𝑋), the space of all sequences (𝑥𝑛), 𝑥𝑛 ∈ 𝑋, 𝑛 = 1, 2, . . . , for which ∑ϕ(‖𝑥𝑛‖) < ∞. Further, extreme, exposed, and smooth points of the unit ball of the space of bounded linear operators on ℓ𝑝, 0 < 𝑝 < 1, are characterized.

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13

Godefroy, Gilles, and Bruno Iochum. "Arens-regularity of Banach algebras and the geometry of Banach spaces." Journal of Functional Analysis 80, no. 1 (September 1988): 47–59. http://dx.doi.org/10.1016/0022-1236(88)90064-x.

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14

Shkarin, S. A. "Isometric embedding of finite ultrametric spaces in Banach spaces." Topology and its Applications 142, no. 1-3 (July 2004): 13–17. http://dx.doi.org/10.1016/j.topol.2003.12.002.

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15

Dilworth, S. J. "Complex convexity and the geometry of Banach spaces." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 3 (May 1986): 495–506. http://dx.doi.org/10.1017/s0305004100064446.

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The notion of PL-convexity was introduced in [4]. In the present article several results are proved which related PL-convexity to various aspects of the geometry of Banach spaces. The first section introduces the moduli of comples convexity and makes a comparison with the more familiar modulus of uniform convexity. It is shown that unconditional convergence of implies convergence of . In the next section the moduli and are shown to be related. The method of proof gives rise to a theorem about strict c-convexity of Lp(X) and a result on the representability in Lp(X).

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16

Selivanov, Yu V. "A problem in the geometry of Banach spaces." Russian Mathematical Surveys 48, no. 4 (August 31, 1993): 251–53. http://dx.doi.org/10.1070/rm1993v048n04abeh001061.

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17

Astashkin, Sergey V., and Fedor A. Sukochev. "Independent functions and the geometry of Banach spaces." Russian Mathematical Surveys 65, no. 6 (December 31, 2010): 1003–81. http://dx.doi.org/10.1070/rm2010v065n06abeh004715.

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18

Haller, Rainis, and Johann Langemets. "Geometry of Banach spaces with an octahedral norm." Acta et Commentationes Universitatis Tartuensis de Mathematica 18, no. 1 (June 25, 2014): 125. http://dx.doi.org/10.12697/acutm.2014.18.13.

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19

Kasparov, Gennadi, and Guoliang Yu. "The Novikov conjecture and geometry of Banach spaces." Geometry & Topology 16, no. 3 (August 27, 2012): 1859–80. http://dx.doi.org/10.2140/gt.2012.16.1859.

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20

Moreno, J. P. "On Geometry of Banach Spaces with Property α." Journal of Mathematical Analysis and Applications 201, no. 2 (July 1996): 600–608. http://dx.doi.org/10.1006/jmaa.1996.0276.

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21

Rasila, Antti, Jarno Talponen, and Xiaohui Zhang. "Observations on quasihyperbolic geometry modeled on Banach spaces." Proceedings of the American Mathematical Society 146, no. 9 (May 24, 2018): 3863–73. http://dx.doi.org/10.1090/proc/13989.

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22

Hájek, P., V. Montesinos, and V. Zizler. "Geometry and Gâteaux smoothness in separable Banach spaces." Operators and Matrices, no. 2 (2012): 201–32. http://dx.doi.org/10.7153/oam-06-15.

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23

Banaś, Józef, and Krzysztof Fra̧czek. "Conditions involving compactness in geometry of Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 20, no. 10 (May 1993): 1217–30. http://dx.doi.org/10.1016/0362-546x(93)90152-i.

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24

Baronti, M., E. Casini, and P. L. Papini. "Antipodal pairs and the geometry of Banach spaces." Rendiconti del Circolo Matematico di Palermo 42, no. 3 (October 1993): 369–81. http://dx.doi.org/10.1007/bf02844628.

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25

Fabian, M., V. Montesinos, and V. Zizler. "Biorthogonal Systems in Weakly Lindelöf Spaces." Canadian Mathematical Bulletin 48, no. 1 (March 1, 2005): 69–79. http://dx.doi.org/10.4153/cmb-2005-006-5.

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26

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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27

Molnár, Lajos, and Borut Zalar. "Reflexivity of the group of surjective isometries on some Banach spaces." Proceedings of the Edinburgh Mathematical Society 42, no. 1 (February 1999): 17–36. http://dx.doi.org/10.1017/s0013091500019982.

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In this paper we study the problem of algebraic reflexivity of the isometry group of some important Banach spaces. Because of the previous work in similar topics, our main interest lies in the von Neumann – Schatten p-classes of compact operators. The ideas developed there can be used in ℓp-spaces, Banach spaces of continuous functions and spin factors as well. Moreover, we attempt to attract the attention to this problem from general Banach spaces geometry view-point. This study, we believe, would provide nice geometrical results.

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28

Rudelson, M., and R. Vershynin. "Embedding Levy families into Banach spaces." Geometric And Functional Analysis 12, no. 1 (May 1, 2002): 183–98. http://dx.doi.org/10.1007/s00039-002-8242-z.

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29

Gowers, W. T. "A new dichotomy for Banach spaces." Geometric and Functional Analysis 6, no. 6 (November 1996): 1083–93. http://dx.doi.org/10.1007/bf02246998.

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30

Polyrakis, Ioannis A. "Strongly exposed points in bases for the positive cone of ordered Banach spaces and characterizations of l1(Г)." Proceedings of the Edinburgh Mathematical Society 29, no. 2 (June 1986): 271–82. http://dx.doi.org/10.1017/s0013091500017648.

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The study of extreme, strongly exposed points of closed, convex and bounded sets in Banach spaces has been developed especially by the interconnection of the Radon–Nikodým property with the geometry of closed, convex and bounded subsets of Banach spaces [5],[2] . In the theory of ordered Banach spaces as well as in the Choquet theory, [4], we are interested in the study of a special type of convex sets, not necessarily bounded, namely the bases for the positive cone. In [7] the geometry (extreme points, dentability) of closed and convex subsets K of a Banach space X with the Radon-Nikodým property is studied and special emphasis has been given to the case where K is a base for acone P of X. In [6, Theorem 1], it is proved that an infinite-dimensional, separable, locally solid lattice Banach space is order-isomorphic to l1 if, and only if, X has the Krein–Milman property and its positive cone has a bounded base.

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31

VEOMETT, E., and K. WILDRICK. "SPACES OF SMALL METRIC COTYPE." Journal of Topology and Analysis 02, no. 04 (December 2010): 581–97. http://dx.doi.org/10.1142/s1793525310000422.

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Mendel and Naor's definition of metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz is equivalent to an ultrametric space having infimal metric cotype 1. We discuss the invariance of metric cotype inequalities under snowflaking mappings and Gromov–Hausdorff limits, and use these facts to establish a partial converse of the main result.

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32

Dodson, C. T. J. "Fréchet geometry via projective limits." International Journal of Geometric Methods in Modern Physics 11, no. 07 (August 2014): 1460017. http://dx.doi.org/10.1142/s0219887814600172.

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Fréchet spaces of sections arise naturally as configurations of a physical field. Some recent work in Fréchet geometry is briefly reviewed and some suggestions for future work are offered. An earlier result on the structure of second tangent bundles in the finite-dimensional case was extended to infinite-dimensional Banach manifolds and Fréchet manifolds that could be represented as projective limits of Banach manifolds. This led to further results concerning the characterization of second tangent bundles and differential equations in the more general Fréchet structure needed for applications.

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33

Duda, Jakub, and Boaz Tsaban. "Null sets and games in Banach spaces." Topology and its Applications 156, no. 1 (November 2008): 56–60. http://dx.doi.org/10.1016/j.topol.2008.04.009.

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34

Angosto, C., and B. Cascales. "Measures of weak noncompactness in Banach spaces." Topology and its Applications 156, no. 7 (April 2009): 1412–21. http://dx.doi.org/10.1016/j.topol.2008.12.011.

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35

JENČOVÁ, ANNA. "QUANTUM INFORMATION GEOMETRY AND NONCOMMUTATIVE Lp-SPACES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 08, no. 02 (June 2005): 215–33. http://dx.doi.org/10.1142/s0219025705001949.

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Let M be a von Neumann algebra. We define the noncommutative extension of information geometry by embeddings of M into noncommutative Lp-spaces. Using the geometry of uniformly convex Banach spaces and duality of the Lp and Lq spaces for 1/p +1/q =1, we show that we can introduce the α-divergence, for α∈(-1, 1), in a similar manner as Amari in the classical case. If restricted to the positive cone, the α-divergence belongs to the class of quasi-entropies, defined by Petz.

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36

Braga, B. M. "Asymptotic structure and coarse Lipschitz geometry of Banach spaces." Studia Mathematica 237, no. 1 (2017): 71–97. http://dx.doi.org/10.4064/sm8604-11-2016.

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37

Fry, R., and S. McManus. "Smooth bump functions and the geometry of banach spaces." Expositiones Mathematicae 20, no. 2 (2002): 143–83. http://dx.doi.org/10.1016/s0723-0869(02)80017-2.

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38

Baronti, M., E. Casini, and P. L. Papini. "On average distances and the geometry of Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 42, no. 3 (October 2000): 533–41. http://dx.doi.org/10.1016/s0362-546x(99)00112-1.

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39

Xu, Genqi, Ji Gao, Peide Liu, and Satit Saejung. "Geometry of Banach Spaces, Operator Theory, and Their Applications." Journal of Function Spaces 2014 (2014): 1. http://dx.doi.org/10.1155/2014/635649.

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40

Dilworth, S. J., Denka Kutzarova, G. Lancien, and N. L. Randrianarivony. "Asymptotic geometry of Banach spaces and uniform quotient maps." Proceedings of the American Mathematical Society 142, no. 8 (April 25, 2014): 2747–62. http://dx.doi.org/10.1090/s0002-9939-2014-12001-6.

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41

Agadzhanov, A. N. "Geometry of norms and inequalities in superreflexive banach spaces." Doklady Mathematics 78, no. 1 (August 2008): 518–21. http://dx.doi.org/10.1134/s1064562408040133.

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42

Ames, W. F., and C. Brezinski. "Geometry of banach spaces, duality mappings and nonlinear problems." Mathematics and Computers in Simulation 34, no. 2 (August 1992): 190. http://dx.doi.org/10.1016/0378-4754(92)90069-s.

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43

Farkas, Bálint, and Henrik Kreidler. "Relative compactness of orbits and geometry of Banach spaces." Journal of Mathematical Analysis and Applications 495, no. 1 (March 2021): 124660. http://dx.doi.org/10.1016/j.jmaa.2020.124660.

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44

Ludkovsky, Sergey V., and Wolfgang Lusky. "On the Geometry of Müntz Spaces." Journal of Function Spaces 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/787291.

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LetΛ={λk}k=1∞satisfy0<λ1<λ2<⋯,∑k=1∞‍1/λk<∞andinfk(λk+1-λk)>0. We investigate the Müntz spacesMpΛ=span¯{tλk:k=1,2,…}⊂Lp(0,1)for1≤p≤∞. We show that, for eachp, there is a Müntz spaceFpwhich contains isomorphic copies of all Müntz spaces as complemented subspaces.Fpis uniquely determined up to isomorphisms by this maximality property. We discuss explicit descriptions ofFp. In particularFpis isomorphic to a Müntz spaceMp(Λ^)whereΛ^consists of positive integers. Finally we show that the Banach spaces(∑n‍⊕Fn)pfor1≤p<∞and(∑n‍⊕Fn)0forp=∞are always isomorphic to suitable Müntz spacesMp(Λ)if theFnare the spans of arbitrary finitely many monomials over[0,1].

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45

Boyd, C., and R. A. Ryan. "THE NORM OF THE PRODUCT OF POLYNOMIALS IN INFINITE DIMENSIONS." Proceedings of the Edinburgh Mathematical Society 49, no. 1 (February 2006): 17–28. http://dx.doi.org/10.1017/s0013091504000756.

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AbstractGiven a Banach space $E$ and positive integers $k$ and $l$ we investigate the smallest constant $C$ that satisfies $\|P\|\hskip1pt\|Q\|\le C\|PQ\|$ for all $k$-homogeneous polynomials $P$ and $l$-homogeneous polynomials $Q$ on $E$. Our estimates are obtained using multilinear maps, the principle of local reflexivity and ideas from the geometry of Banach spaces (type and uniform convexity). We also examine the analogous problem for general polynomials on Banach spaces.

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46

Goldstein, Jerome A., Shinnosuke Oharu, and Andrew Vogt. "Affine semigroups on Banach spaces." Hiroshima Mathematical Journal 18, no. 2 (1988): 433–50. http://dx.doi.org/10.32917/hmj/1206129734.

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47

Friedman, Yaakov, and Bernard Russo. "Affine structure of facially symmetric spaces." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 1 (July 1989): 107–24. http://dx.doi.org/10.1017/s030500410006802x.

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In [7], the authors proposed the problem of giving a geometric characterization of those Banach spaces which admit an algebraic structure. Motivated by the geometry imposed by measuring processes on the set of observables of a quantum mechanical system, they introduced the category of facially symmetric spaces. A discrete spectral theorem for an arbitrary element in the dual of a reflexive facially symmetric space was obtained by using the basic notions of orthogonality, protective unit, norm exposed face, symmetric face, generalized tripotent and generalized Peirce projection, which were introduced and developed in this purely geometric setting.

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48

Johson, W. B., J. Lindenstrauss, and G. Schechtman. "Banach spaces determined by their uniform structures." Geometric and Functional Analysis 6, no. 3 (May 1996): 430–70. http://dx.doi.org/10.1007/bf02249259.

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49

Botelho, G., D. Diniz, V. V. Fávaro, and D. Pellegrino. "Spaceability in Banach and quasi-Banach sequence spaces." Linear Algebra and its Applications 434, no. 5 (March 2011): 1255–60. http://dx.doi.org/10.1016/j.laa.2010.11.012.

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50

Smith, Richard J. "Topology, isomorphic smoothness and polyhedrality in Banach spaces." Topology and its Applications 266 (October 2019): 106848. http://dx.doi.org/10.1016/j.topol.2019.106848.

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