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Fragmentability and \(\sigma\)-fragmentability. (English) Zbl 0801.46011

Summary: Recent work has studied the fragmentability and \(\sigma\)-fragmentability properties of Banach spaces. Here examples are given that justify the definitions that have been used. The fragmentability and \(\sigma\)- fragmentability properties of the spaces \(\ell^ \infty\) and \(\ell_ c^ \infty (\Gamma)\), with \(\Gamma\) uncountable, are determined.

MSC:

46B26 Nonseparable Banach spaces
46B20 Geometry and structure of normed linear spaces

Keywords:

fragmentability
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