Jayne, J. E.; Namioka, I.; Rogers, C. A. \(\sigma\)-fragmented Banach spaces. II. (English) Zbl 0807.46020 Stud. Math. 111, No. 1, 69-80 (1994). Summary: 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.[For part I see Mathematika 39, No. 1, 161-188, and No. 2, 197-215 (1992; Zbl 0761.46008 and Zbl 0761.46009)]. Cited in 3 Documents MSC: 46B26 Nonseparable Banach spaces Keywords:\(\sigma\)-fragmented Banach spaces; norming \(M\)-basis; locally uniformly convex norms Citations:Zbl 0761.46008; Zbl 0761.46009 PDFBibTeX XMLCite \textit{J. E. Jayne} et al., Stud. Math. 111, No. 1, 69--80 (1994; Zbl 0807.46020) Full Text: DOI EuDML