SIGMA-FRAGMENTED BANACH-SPACES .2.

Recent papers have investigated the properties of sigma-fragmented Ban ach spaces and have sought to find which Banach spaces are sigma-fragm ented and which are not. Banach spaces that have a norming M-basis are shown to be sigma-fragmented using weakly closed sets. Zizler has sho wn that Banach spaces satisfying certain conditions have locally unifo rmly convex norms. Banach spaces that satisfy similar, but weaker cond itions 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 s ets.