Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Antonis Manoussakis, Anna Pelczar-Barwacz, Michał Świȩtek
by Bentuo Zheng (bzheng) 01 Oct '16

01 Oct '16

This is an announcement for the paper “Unconditionally saturated Banach space with the scalar-plus-compact property” by Antonis Manoussakis<https://arxiv.org/find/math/1/au:+Manoussakis_A/0/1/0/all/0/1>, Anna Pelczar-Barwacz<https://arxiv.org/find/math/1/au:+Pelczar_Barwacz_A/0/1/0/all/0/1>, Michał Świȩtek<https://arxiv.org/find/math/1/au:+Swietek_M/0/1/0/all/0/1>. Abstract: We construct a Bourgain-Delbaen $\mathcal{L}_\infty$-space $\mathcal{X}_{kus}$ with strongly heterogenous structure: any bounded operator on $\mathcal{X}_{kus}$ is a compact perturbation of a multiple of the identity, whereas the space $\mathcal{X}_{kus}$ is saturated with unconditional basic sequences. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.06506

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Abstract of a paper by Jahangir Cheshmavar, Sayed Kamel Hosseini
by Bentuo Zheng (bzheng) 01 Oct '16

01 Oct '16

This is an announcement for the paper “Commutative Banach algebra generated by the Lambert multipliers with some new properties” by Jahangir Cheshmavar<https://arxiv.org/find/math/1/au:+Cheshmavar_J/0/1/0/all/0/1>, Sayed Kamel Hosseini<https://arxiv.org/find/math/1/au:+Hosseini_S/0/1/0/all/0/1>. Abstract: The set of all Lambert multipliers acting between $L_p$-spaces are Banach spaces. In this paper, we show that such multipliers are commutative Banach algebra. Also we present some new properties of this spaces. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.06075

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Abstract of a paper by Eusebio Gardella, Hannes Thiel
by Bentuo Zheng (bzheng) 01 Oct '16

01 Oct '16

This is an announcement for the paper “Preduals and complementation of spaces of bounded linear operators” by Eusebio Gardella<https://arxiv.org/find/math/1/au:+Gardella_E/0/1/0/all/0/1>, Hannes Thiel<https://arxiv.org/find/math/1/au:+Thiel_H/0/1/0/all/0/1>. Abstract: For Banach spaces $X$ and $Y$, we establish a natural bijection between preduals of $Y$ and preduals of $L(X,Y)$ that respect the right $L(X)$-module structure. If $X$ is reflexive, it follows that there is a unique predual making $L(X)$ into a dual Banach algebra. This removes the condition that $X$ have the approximation property in a result of Daws. We further establish a natural bijection between projections that complement $Y$ in its bidual and projections that complement $L(X,Y)$ in its bidual as a right $L(X)$-module. It follows that $Y$ is complemented in its bidual if and only if $L(X,Y)$ is complemented in its bidual (either as a module or as a Banach space). The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.05326

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Abstract of a paper by Daniele Puglisi
by Bentuo Zheng (bzheng) 01 Oct '16

01 Oct '16

This is an announcement for the paper “Operators on Bourgain-Delbaen's spaces” by Daniele Puglisi<https://arxiv.org/find/math/1/au:+Puglisi_D/0/1/0/all/0/1>. Abstract: We prove that, for a suitable choice of real numbers $a, b$, every operator from $\ell_2$ to $X_{a, b}$ and from $X_{a,b}$ to $\ell_2$ must be compact, where $X_{a,b}$ is the Bourgain- Delbaen's space. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.03270

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Abstract of a paper by Pilar Rueda, Enrique A. Sanchez-Perez
by Bentuo Zheng (bzheng) 01 Oct '16

01 Oct '16

This is an announcement for the paper “The approximation property and Lipschitz mappings on Banach spacess” by Pilar Rueda<https://arxiv.org/find/math/1/au:+Rueda_P/0/1/0/all/0/1>, Enrique A. Sanchez-Perez<https://arxiv.org/find/math/1/au:+Sanchez_Perez_E/0/1/0/all/0/1>. Abstract: We present an overview to the approximation property, paying especial attention to the recent results relating the approximation property to ideals of linear operators and Lipschitz ideals. We complete the paper with some new results on approximation of Lipschitz mappings and their relation to linear operator ideals. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.02707

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Abstract of a paper by Antonio Avilés, Piotr Koszmider
by Bentuo Zheng (bzheng) 01 Oct '16

01 Oct '16

This is an announcement for the paper “A 1-separably injective space that does not contain $\ell_\infty$” by Antonio Avilés<https://arxiv.org/find/math/1/au:+Aviles_A/0/1/0/all/0/1>, Piotr Koszmider<https://arxiv.org/find/math/1/au:+Koszmider_P/0/1/0/all/0/1>. Abstract: We study the $\omega_2$-subsets of tightly $\sigma$-filtered Boolean algebras and, as an application, we show the consistency of the existence of a Banach space that is $1$-separably injective but does not contain any isomorphic copy of $\ell_\infty$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.02685

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Abstract of a paper by Johann Langemets, Vegard Lima, Abraham Rueda Zoca
by Bentuo Zheng (bzheng) 01 Oct '16

01 Oct '16

This is an announcement for the paper “Octahedral norms in tensor products of Banach spaces” by Johann Langemets<https://arxiv.org/find/math/1/au:+Langemets_J/0/1/0/all/0/1>, Vegard Lima<https://arxiv.org/find/math/1/au:+Lima_V/0/1/0/all/0/1>, Abraham Rueda Zoca<https://arxiv.org/find/math/1/au:+Zoca_A/0/1/0/all/0/1>. Abstract: We continue the investigation of the behaviour of octahedral norms in tensor products of Banach spaces. Firstly, we will prove the existence of a Banach space Y such that the injective tensor products $\ell_1\hat{\otimes_{\epsilon}} Y$ and $L_1\hat{\otimes_{\epsilon}} Y$ both fail to have an octahedral norm. Secondly, we will show that in the presence of the metric approximation property octahedrality is preserved from one of the factors by taking projective tensor products with an arbitrary Banach space. These results show how octahedrality is preserved by injective and projective tensor products and solve open problems from the literature. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.02062

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Abstract of a paper by M De la Sen
by Bentuo Zheng (bzheng) 01 Oct '16

01 Oct '16

This is an announcement for the paper “Preliminaries on CAT (0) Spaces and Fixed Points of a Class of Iterative Schemes” by M De la Sen<https://arxiv.org/find/math/1/au:+Sen_M/0/1/0/all/0/1>. Abstract: This paper gives some relating results for various concepts of convexity in metric spaces such as midpoint convexity, convex structure, uniform convexity and near-uniform convexity, Busemann curvature and its relation to convexity. Some properties of uniform convexity and near uniform convexity of geodesic metric spaces are related to the mapping built with the concourse of two primary mappings and the associated generated sequences by some iterative schemes. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.01927

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Abstract of a paper by Grigiry Ivanov, Horst Martini
by Bentuo Zheng (bzheng) 01 Oct '16

01 Oct '16

This is an announcement for the paper “New Moduli for Banach Spaces” by Grigiry Ivanov<https://arxiv.org/find/math/1/au:+Ivanov_G/0/1/0/all/0/1>, Horst Martini<https://arxiv.org/find/math/1/au:+Martini_H/0/1/0/all/0/1>. Abstract: Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, e.g., as lengths of catheti of right-angled triangles (defined via so-called quasi-orthogonality). These triangles have two boundary points of the unit ball of a Banach space as endpoints of their hypotenuse, and their third vertex lies in a supporting hyperplane of one of the two other vertices. Among other things it is our goal to quantify via such triangles the local deviation of the unit sphere from its supporting hyperplanes. We prove respective Day-Nordlander type results, involving generalizations of the modulus of convexity and the modulus of Bana\'{s}. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.01587

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Announcement of a paper by Luigi Ambrosio, Daniele Puglisi
by Bentuo Zheng (bzheng) 01 Oct '16

01 Oct '16

This is an announcement for the paper “Linear extension operators between spaces of Lipschitz maps and optimal transport” by Luigi Ambrosio<https://arxiv.org/find/math/1/au:+Ambrosio_L/0/1/0/all/0/1>, Daniele Puglisi<https://arxiv.org/find/math/1/au:+Puglisi_D/0/1/0/all/0/1>. Abstract: Motivated by the notion of $K$-gentle partition of unity introduced in [12] and the notion of $K$-Lipschitz retract studied in [17], we study a weaker notion related to the Kantorovich-Rubinstein transport distance, that we call $K$-random projection. We show that $K$-random projections can still be used to provide linear extension operators for Lipschitz maps. We also prove that the existence of these random projections is necessary and sufficient for the existence of weak$^*$ continuous operators. Finally we use this notion to characterize the metric spaces $(X, d)$ such that the free space $F(X)$ has the bounded approximation propriety. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.01450

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