Topology, isomorphic smoothness and polyhedrality in Banach spaces

Preprint English OPEN
Smith, Richard J. (2018)
  • Subject: 46B03, 46B20, 46B26 | Mathematics - Functional Analysis
    arxiv: Mathematics::Functional Analysis

In recent decades, topology has come to play an increasing role in some geometric aspects of Banach space theory. The class of so-called $w^*$-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.
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