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Journal articles on the topic 'Banach spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 July 2024

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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

Saleh Hamarsheh, A. "k-Smooth Points in Some Banach Spaces." International Journal of Mathematics and Mathematical Sciences 2015 (2015): 1–4. http://dx.doi.org/10.1155/2015/394282.

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We characterize thek-smooth points in some Banach spaces. We will deal with injective tensor product, the Bochner spaceL∞(μ,X)of (equivalence classes of)μ-essentially bounded measurableX-valued functions, and direct sums of Banach spaces.

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3

Agarwal, Ravi P., and Donal O'Regan. "Leray-Schauder results for multivalued nonlinear contractions defined on closed subsets of a Fréchet space." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–8. http://dx.doi.org/10.1155/ijmms/2006/43635.

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New Leray-Schauder results are presented for multivalued contractions defined on subsets of a Fréchet spaceE. The proof relies on fixed point results in Banach spaces and on viewingEas the projective limit of a sequence of Banach spaces.

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4

Werner, Dirk. "Indecomposable Banach spaces." Acta et Commentationes Universitatis Tartuensis de Mathematica 5 (December 31, 2001): 89–105. http://dx.doi.org/10.12697/acutm.2001.05.08.

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This paper aims at describing Tim Gowers' contributions to Banach space theory that earned him the Fields medal in 1998. In particular, the construction of the Gowers-Maurey space, a Banach space not containing an unconditional basic sequence, is sketched as is the Gowers dichotomy theorem that led to the solution of the homogeneous Banach space problem. Moreover, Gowers' counterexamples to the hyperplane problem and the Schröder-Bernstein problem are discussed. The paper is an extended version of a talk given at Freie Universität Berlin in December 1999; hence the reference to the next millennium at the very end actually appeals to the present millennium. It should be accessible to anyone with a basic knowledge of functional analysis and of German.

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5

Kusraev, A. G. "Banach-Kantorovich spaces." Siberian Mathematical Journal 26, no. 2 (1985): 254–59. http://dx.doi.org/10.1007/bf00968770.

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6

Oikhberg, T., and E. Spinu. "Subprojective Banach spaces." Journal of Mathematical Analysis and Applications 424, no. 1 (April 2015): 613–35. http://dx.doi.org/10.1016/j.jmaa.2014.11.008.

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7

González, Manuel, and Javier Pello. "Superprojective Banach spaces." Journal of Mathematical Analysis and Applications 437, no. 2 (May 2016): 1140–51. http://dx.doi.org/10.1016/j.jmaa.2016.01.033.

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8

Qiu, Jing Hui, and Kelly McKennon. "Banach-Mackey spaces." International Journal of Mathematics and Mathematical Sciences 14, no. 2 (1991): 215–19. http://dx.doi.org/10.1155/s0161171291000224.

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In recent publications the concepts of fast completeness and local barreledness have been shown to be related to the property of all weak-*bounded subsets of the dual (of a locally convex space) being strongly bounded. In this paper we clarify those relationships, as well as giving several different characterizations of this property.

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9

Dineen, Seán, and Michael Mackey. "Confined Banach spaces." Archiv der Mathematik 87, no. 3 (September 2006): 227–32. http://dx.doi.org/10.1007/s00013-006-1693-y.

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10

Ferenczi, Valentin, and Christian Rosendal. "Ergodic Banach spaces." Advances in Mathematics 195, no. 1 (August 2005): 259–82. http://dx.doi.org/10.1016/j.aim.2004.08.008.

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11

Bastero, Jesús. "Embedding unconditional stable banach spaces into symmetric stable banach spaces." Israel Journal of Mathematics 53, no. 3 (December 1986): 373–80. http://dx.doi.org/10.1007/bf02786569.

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12

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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13

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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14

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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15

Hõim, Terje, and David A. Robbins. "Banach-Stone theorems for Banach bundles." Acta et Commentationes Universitatis Tartuensis de Mathematica 9 (December 31, 2005): 65–76. http://dx.doi.org/10.12697/acutm.2005.09.08.

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We prove two Banach-Stone type theorems for section spaces of real Banach bundles. The first theorem assumes that the duals of all fibers are strictly convex, and the second considers disjointness-preserving operators. In each case, the result generalizes the corresponding Banach-Stone theorem for spaces of continuous vector-valued functions.

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16

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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17

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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18

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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19

Lima, Vegard. "Approximation properties for dual spaces." MATHEMATICA SCANDINAVICA 93, no. 2 (December 1, 2003): 297. http://dx.doi.org/10.7146/math.scand.a-14425.

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We prove that a Banach space $X$ has the metric approximation property if and only if $\mathcal F(Y,X)$ is an ideal in $\mathcal L(Y,X^{**})$ for all Banach spaces $Y$. Furthermore, $X^*$ has the metric approximation property if and only if for all Banach spaces $Y$ and all Hahn-Banach extension operators $\phi : X^* \rightarrow X^{***}$ there exists a Hahn-Banach extension operator $\Phi : {\mathcal F(Y,X)}^* \rightarrow {\mathcal L(Y,X^{**})}^*$ such that $\Phi(x^* \otimes y^{**}) = (\phi x^*) \otimes y^{**}$ for all $x^* \in X^*$ and all $y^{**} \in Y^{**}$. We also prove that $X^*$ has the approximation property if and only if for all Banach spaces $Y$ and all Hahn-Banach extension operators $\phi : X^* \rightarrow X^{***}$ there exists a Hahn-Banach extension operator $\Phi : {\mathcal F(Y,X)}^* \rightarrow {\mathcal W(Y,X^{**})}^*$ such that $\Phi(x^* \otimes y^{**}) = (\phi x^*) \otimes y^{**}$ for all $x^* \in X^*$ and all $y^{**} \in Y^{**}$, which in turn is equivalent to $\mathcal F(Y,\hat{X})$ being an ideal in $\mathcal W(Y,\hat{X}^{**})$ for all Banach spaces $Y$ and all equivalent renormings $\hat{X}$ of $X$.

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20

Wulede, Suyalatu, and Wudunqiqige Ha. "A new class of Banach space with the drop property." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 1 (January 30, 2012): 215–24. http://dx.doi.org/10.1017/s0308210510000545.

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We discuss a new class of Banach spaces which are wider than the strongly convex spaces introduced by Congxin Wu and Yongjin Li. We prove that the new class of Banach spaces lies strictly between either the class of uniformly convex spaces and strongly convex spaces or the class of fully k-convex spaces and strongly convex spaces. The new class of Banach spaces has inclusive relations with neither the class of locally uniformly convex spaces nor the class of nearly uniformly convex spaces. We obtain in addition some characterizations of this new class of Banach spaces.

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21

Manhas, J. S. "Composition Operators and Multiplication Operators on Weighted Spaces of Analytic Functions." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–21. http://dx.doi.org/10.1155/2007/92070.

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LetVbe an arbitrary system of weights on an open connected subsetGofℂN(N≥1)and letB(E)be the Banach algebra of all bounded linear operators on a Banach spaceE. LetHVb(G,E)andHV0(G,E)be the weighted locally convex spaces of vector-valued analytic functions. In this survey, we present a development of the theory of multiplication operators and composition operators from classical spaces of analytic functionsH(G)to the weighted spaces of analytic functionsHVb(G,E)andHV0(G,E).

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22

SHEKHAR, CHANDER, TARA ., and GHANSHYAM SINGH RATHORE. "RETRO K-BANACH FRAMES IN BANACH SPACES." Poincare Journal of Analysis and Applications 05, no. 2.1 (December 30, 2018): 65–75. http://dx.doi.org/10.46753/pjaa.2018.v05i02(i).003.

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23

Kaushik, Shiv K., and Varinder Kumar. "On fusion frames in Banach spaces." gmj 18, no. 1 (August 5, 2010): 121–30. http://dx.doi.org/10.1515/gmj.2010.029.

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Abstract A necessary and sufficient condition for a complete sequence of subspaces to be a fusion Banach frame for E is given. Also, we introduce fusion Banach frame sequences and give a characterization for a complete sequence of subspaces of E to be a fusion Banach frame for E in terms of fusion Banach frame sequences. Finally, along with other results, we characterize fusion Banach frames in terms of Banach frames.

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24

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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25

Caetano, António, Amiran Gogatishvili, and Bohumír Opic. "Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 146, no. 5 (June 23, 2016): 905–27. http://dx.doi.org/10.1017/s0308210515000761.

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There are two main aims of the paper. The first is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second is to extend the criterion for the precompactness of sets in the Lebesgue spaces Lp(ℝn), 1 ⩽ p < ∞, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces , into Lorentz-type spaces.

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26

Pang, Chin-Tzong, and Eskandar Naraghirad. "Approximating Common Fixed Points of Bregman Weakly Relatively Nonexpansive Mappings in Banach Spaces." Journal of Function Spaces 2014 (2014): 1–19. http://dx.doi.org/10.1155/2014/743279.

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Using Bregman functions, we introduce a new hybrid iterative scheme for finding common fixed points of an infinite family of Bregman weakly relatively nonexpansive mappings in Banach spaces. We prove a strong convergence theorem for the sequence produced by the method. No closedness assumption is imposed on a mappingT:C→C, whereCis a closed and convex subset of a reflexive Banach spaceE. Furthermore, we apply our method to solve a system of equilibrium problems in reflexive Banach spaces. Some application of our results to the problem of finding a minimizer of a continuously Fréchet differentiable and convex function in a Banach space is presented. Our results improve and generalize many known results in the current literature.

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27

Dobrakov, Ivan, and Pedro Morales. "On integration in Banach spaces, VI." Czechoslovak Mathematical Journal 35, no. 2 (1985): 173–87. http://dx.doi.org/10.21136/cmj.1985.102009.

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28

Dobrakov, Ivan. "On integration in Banach spaces, VII." Czechoslovak Mathematical Journal 38, no. 3 (1988): 434–49. http://dx.doi.org/10.21136/cmj.1988.102239.

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29

JAIN, P. K., S. K. KAUSHIK, and NISHA GUPTA. "ON NEAR EXACT BANACH FRAMES IN BANACH SPACES." Bulletin of the Australian Mathematical Society 78, no. 2 (October 2008): 335–42. http://dx.doi.org/10.1017/s0004972708000889.

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AbstractNear exact Banach frames are introduced and studied, and examples demonstrating the existence of near exact Banach frames are given. Also, a sufficient condition for a Banach frame to be near exact is obtained. Further, we consider block perturbation of retro Banach frames, and prove that a block perturbation of a retro Banach frame is also a retro Banach frame. Finally, it is proved that if E and F are both Banach spaces having Banach frames, then the product space E×F has an exact Banach frame.

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30

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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31

Kaushik, S. K. "Some results concerning frames in Banach spaces." Tamkang Journal of Mathematics 38, no. 3 (September 30, 2007): 267–76. http://dx.doi.org/10.5556/j.tkjm.38.2007.80.

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A necessary and sufficient condition for the associated sequence of functionals to a complete minimal sequence to be a Banach frame has been given. We give the definition of a weak-exact Banach frame, and observe that an exact Banach frame is weak-exact. An example of a weak-exact Banach frame which is not exact has been given. A necessary and sufficient condition for a Banach frame to be a weak-exact Banach frame has been obtained. Finally, a necessary condition for the perturbation of a retro Banach frame by a finite number of linearly independent vectors to be a retro Banach frame has been given.

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32

Castillo, Jesús. "The hitchhiker guide to Categorical Banach space theory. Part II." Extracta Mathematicae 37, no. 1 (June 1, 2022): 1–56. http://dx.doi.org/10.17398/2605-5686.37.1.1.

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What has category theory to offer to Banach spacers? In this second part survey-like paper we will focus on very much needed advanced categorical and homological elements, such as Kan extensions, derived category and derived functor or Abelian hearts of Banach spaces.

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33

Godefroy, G., and N. J. Kalton. "Lipschitz-free Banach spaces." Studia Mathematica 159, no. 1 (2003): 121–41. http://dx.doi.org/10.4064/sm159-1-6.

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34

Wojtowicz, Marek. "Finitely Nonreflexive Banach Spaces." Proceedings of the American Mathematical Society 106, no. 4 (August 1989): 961. http://dx.doi.org/10.2307/2047280.

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35

Lin, Bor-Luh, and T. S. S. R. K. Rao. "Multismoothness in Banach Spaces." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–12. http://dx.doi.org/10.1155/2007/52382.

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In this paper, motivated by the results published by R. Khalil and A. Saleh in 2005, we study the notion ofk-smooth points and the notion ofk-smoothness, which are dual to the notion ofk-rotundity. Generalizing these notions and combining smoothness with the recently introduced notion of unitary, we study classes of Banach spaces for which the vector space, spanned by the state space corresponding to a unit vector, is a closed set.

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36

Casazza, P. G., and M. C. Lammers. "Genus $n$ Banach spaces." Illinois Journal of Mathematics 43, no. 2 (June 1999): 307–23. http://dx.doi.org/10.1215/ijm/1255985217.

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37

Lindenstrauss, Joram. "BANACH SPACES FOR ANALYSTS." Bulletin of the London Mathematical Society 24, no. 6 (November 1992): 620–22. http://dx.doi.org/10.1112/blms/24.6.620.

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38

Jayne, J. E., I. Namioka, and C. A. Rogers. "σ‐fragmentable Banach spaces." Mathematika 39, no. 1 (June 1992): 161–88. http://dx.doi.org/10.1112/s0025579300006926.

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Jayne, J. E., I. Namioka, and C. A. Rogers. "σ‐fragmentable Banach spaces." Mathematika 39, no. 2 (December 1992): 197–215. http://dx.doi.org/10.1112/s0025579300014935.

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40

Gilles, Godefroy. "Lipschitz approximable Banach spaces." Commentationes Mathematicae Universitatis Carolinae 61, no. 2 (November 5, 2020): 187–93. http://dx.doi.org/10.14712/1213-7243.2020.021.

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41

W{ójtowicz, Marek. "Finitely nonreflexive Banach spaces." Proceedings of the American Mathematical Society 106, no. 4 (April 1, 1989): 961. http://dx.doi.org/10.1090/s0002-9939-1989-0949882-0.

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42

Moreno, Yolanda, and Anatolij Plichko. "On automorphic Banach spaces." Israel Journal of Mathematics 169, no. 1 (November 22, 2008): 29–45. http://dx.doi.org/10.1007/s11856-009-0002-4.

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43

Bandyopadhyay, Pradipta, Yongjin Li, Bor-Luh Lin, and Darapaneni Narayana. "Proximinality in Banach spaces." Journal of Mathematical Analysis and Applications 341, no. 1 (May 2008): 309–17. http://dx.doi.org/10.1016/j.jmaa.2007.10.024.

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44

Rosenthal, Haskell. "Weak∗-Polish Banach spaces." Journal of Functional Analysis 76, no. 2 (February 1988): 267–316. http://dx.doi.org/10.1016/0022-1236(88)90039-0.

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45

Klimek, Slawomir, and Andrzej Lesniewski. "Pfaffians on Banach spaces." Journal of Functional Analysis 102, no. 2 (December 1991): 314–30. http://dx.doi.org/10.1016/0022-1236(91)90124-n.

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46

Abrahamsen, Trond A., Johann Langemets, and Vegard Lima. "Almost square Banach spaces." Journal of Mathematical Analysis and Applications 434, no. 2 (February 2016): 1549–65. http://dx.doi.org/10.1016/j.jmaa.2015.09.060.

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47

Raja, M. "Super WCG Banach spaces." Journal of Mathematical Analysis and Applications 439, no. 1 (July 2016): 183–96. http://dx.doi.org/10.1016/j.jmaa.2016.02.057.

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48

Aron, Richard M., and Seán Dineen. "$Q$-Reflexive Banach Spaces." Rocky Mountain Journal of Mathematics 27, no. 4 (December 1997): 1009–25. http://dx.doi.org/10.1216/rmjm/1181071856.

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49

James, R. C. "Some Interesting Banach Spaces." Rocky Mountain Journal of Mathematics 23, no. 3 (September 1993): 911–37. http://dx.doi.org/10.1216/rmjm/1181072532.

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Bandyopadhyay, Pradipta, Krzysztof Jarosz, and T. S. S. R. K. Rao. "Unitaries in Banach spaces." Illinois Journal of Mathematics 48, no. 1 (January 2004): 339–51. http://dx.doi.org/10.1215/ijm/1258136187.

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