Boundaries and polyhedral Banach spaces

Vladimir P Fonf; Richard J Smith; Stanimir Troyanski

doi:10.1090/proc/12644

Boundaries and polyhedral Banach spaces

Functional Analysis 2022-06-14 v1

Authors: Vladimir P Fonf , Richard J Smith , Stanimir Troyanski

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Abstract

We show that if $X$ and $Y$ are Banach spaces, where $Y$ is separable and polyhedral, and if $T:X \to Y$ 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.

Keywords

operator theory on banach spaces banach spaces banach algebras

Cite

@article{arxiv.1404.1185,
  title  = {Boundaries and polyhedral Banach spaces},
  author = {Vladimir P Fonf and Richard J Smith and Stanimir Troyanski},
  journal= {arXiv preprint arXiv:1404.1185},
  year   = {2022}
}

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