## σ-fragmented Banach spaces II

### Volume 111 / 1994

Studia Mathematica 111 (1994), 69-80
DOI: 10.4064/sm-111-1-69-80

#### Abstract

Recent papers have investigated the properties of σ-fragmented Banach spaces and have sought to find which Banach spaces are σ-fragmented and which are not. Banach spaces that have a norming M-basis are shown to be σ-fragmented using weakly closed sets. Zizler has shown that Banach spaces satisfying certain conditions have locally uniformly convex norms. Banach spaces that satisfy similar, but weaker conditions are shown to be σ-fragmented. An example, due to R. Pol, is given of a Banach space that is σ-fragmented using differences of weakly closed sets, but is not σ-fragmented using weakly closed sets.