Boundaries and polyhedral banach spaces

V. P. Fonf; R. J. Smith; S. Troyanski

doi:10.1090/proc/12644

Boundaries and polyhedral banach spaces

V. P. Fonf, R. J. Smith, S. Troyanski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We show that if X and Y are Banach spaces, where Y is separable and polyhedral, and if T : X → Y is a bounded linear operator such that T∗(Y ∗) contains a boundary B of X, then X is separable and isomorphic to a polyhedral space. Some corollaries of this result are presented.

Original language	English
Pages (from-to)	4845-4849
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	11
DOIs	https://doi.org/10.1090/proc/12644
State	Published - 1 Nov 2015

Keywords

Boundaries
Polyhedral norms
Polytopes
Renormings

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/proc/12644

Cite this

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abstract = "We show that if X and Y are Banach spaces, where Y is separable and polyhedral, and if T : X → Y is a bounded linear operator such that T∗(Y ∗) contains a boundary B of X, then X is separable and isomorphic to a polyhedral space. Some corollaries of this result are presented.",

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AU - Fonf, V. P.

AU - Smith, R. J.

AU - Troyanski, S.

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N2 - We show that if X and Y are Banach spaces, where Y is separable and polyhedral, and if T : X → Y is a bounded linear operator such that T∗(Y ∗) contains a boundary B of X, then X is separable and isomorphic to a polyhedral space. Some corollaries of this result are presented.

AB - We show that if X and Y are Banach spaces, where Y is separable and polyhedral, and if T : X → Y is a bounded linear operator such that T∗(Y ∗) contains a boundary B of X, then X is separable and isomorphic to a polyhedral space. Some corollaries of this result are presented.

KW - Boundaries

KW - Polyhedral norms

KW - Polytopes

KW - Renormings

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DO - 10.1090/proc/12644

M3 - Article

AN - SCOPUS:84940404117

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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Boundaries and polyhedral banach spaces

Abstract

Keywords

ASJC Scopus subject areas

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