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On a difference between quantitative weak sequential completeness and the quantitative Schur property

Abstract

We study quantitative versions of the Schur property and weak sequential completeness, proceeding thus with investigations started by G. Godefroy, N. Kalton and D. Li and continued by H. Pfitzner and the authors. We show that the Schur property of $\ell_1$ holds quantitatively in the strongest possible way and construct an example of a Banach space which is quantitatively weakly sequentially complete, has the Schur property but fails the quantitative form of the Schur property.Comment: 10 pages, the paper was slightly reorganized, some more comments were adde

Topics: Mathematics - Functional Analysis, 46B20, 46B25
Year: 2011
DOI identifier: 10.1090/S0002-9939-2012-11175-X
OAI identifier: oai:arXiv.org:1103.2975