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On quantification of weak sequential completeness

Abstract : We consider several quantities related to weak sequential com- pleteness of a Banach space and prove some of their properties in general and in L-embedded Banach spaces, improving in particular an inequality of G. Godefroy, N. Kalton and D. Li. We show some examples witnessing natural limits of our positive results, in particular, we construct a separable Banach space X with the Schur property that cannot be renormed to have a certain quantitative form of weak sequential completeness, thus providing a partial answer to a question of G. Godefroy.
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Submitted on : Wednesday, December 8, 2010 - 5:03:09 PM
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Ondrej Kalenda, Hermann Pfitzner, Jiri Spurny. On quantification of weak sequential completeness. Journal of Functional Analysis, Elsevier, 2011, 260 (10), pp.2986-2996. ⟨hal-00544711⟩

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