Topology, isomorphic smoothness and polyhedrality in Banach spaces

Abstract

In recent decades, topology has come to play an increasing role in some geometric aspects of Banach space theory. The class of so-called $w^{\ast }$-locally relatively compact sets was introduced recently by Fonf, Pallares, Troyanski and the author, and were found to be a useful topological tool in the theory of isomorphic smoothness and polyhedrality in Banach spaces. We develop the topological theory of these sets and present some Banach space applications.

References in corpus (5)

• Polyhedrality in Pieces
• Smooth and polyhedral approximation in Banach spaces
• Using boundaries to find smooth norms
• Approximation of norms on Banach spaces
• Chains of functions in $C(K)$-spaces

Cited by in corpus (1)

• Smooth and polyhedral norms via fundamental biorthogonal systems