Boundaries and polyhedral Banach spaces

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 $T^{\ast }(Y^{\ast })$ contains a boundary $B$ of $X$, then $X$ is separable and isomorphic to a polyhedral space. Some corollaries of this result are presented.

Cited by in corpus (2)

• Smooth and polyhedral approximation in Banach spaces
• Polyhedrality and decomposition