SIGMA-FRAGMENTED BANACH-SPACES .2.

Recent papers have investigated the properties of sigma-fragmented Banach spaces and have sought to find which Banach spaces are sigma-fragmented and which are not. Banach spaces that have a norming M-basis are shown to be sigma-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 sigma-fragmented. An example, due to R. Pol, is given of a Banach space that is sigma-fragmented using differences of weakly closed sets, but is not sigma-fragmented using weakly closed sets.