On quantification of weak sequential completeness

Details On quantification of weak sequential completeness On quantification of weak sequential completeness

2010-11-30

arxiv.org/abs/1011.6553v1

J. Funct. Anal. 260 (2011), no. 10, 2986-2996

Mathematics

Functional Analysis

9 pages

Scientific paper

10.1016/j.jfa.2011.02.006

We consider several quantities related to weak sequential completeness 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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