Boundaries and polyhedral Banach spaces

Abstract

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