Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840447 | Nonlinear Analysis: Theory, Methods & Applications | 2012 | 6 Pages |
Abstract
We study the stability properties of the class of weak*-extensible spaces introduced by Wang, Zhao, and Qiang showing, among other things, that weak*-extensibility is equivalent to having a weak*-sequentially continuous dual ball (in short, w*SC) for duals of separable spaces or twisted sums of w*SC spaces. This shows that weak*-extensibility is not a 33-space property, solving a question posed by Wang, Zhao, and Qiang. We also introduce a restricted form of weak*-extensibility, called separable weak*-extensibility, and show that separably weak*-extensible Banach spaces have the Gelfand–Phillips property, although they are not necessarily w*SC spaces.
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Authors
Jesús M.F. Castillo, Manuel González, Pier Luigi Papini,