On quantification of weak sequential completeness |
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Authors: | OFK Kalenda |
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Institution: | a Department of Mathematical Analysis, Faculty of Mathematics and Physic, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic b Université d?Orléans, BP 6759, F-45067 Orléans Cedex 2, France |
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Abstract: | 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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Keywords: | Weakly sequentially complete Banach space L-embedded Banach space Quantitative versions of weak sequential completeness |
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