On a difference between quantitative weak sequential completeness and the quantitative Schur property
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- by O. F. K. Kalenda and J. Spurný PDF
- Proc. Amer. Math. Soc. 140 (2012), 3435-3444 Request permission
Abstract:
We study quantitative versions of the Schur property and weak sequential completeness, proceeding 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.References
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Additional Information
- O. F. K. Kalenda
- Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic
- ORCID: 0000-0003-4312-2166
- Email: kalenda@karlin.mff.cuni.cz
- J. Spurný
- Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic
- Email: spurny@karlin.mff.cuni.cz
- Received by editor(s): March 15, 2011
- Received by editor(s) in revised form: April 5, 2011
- Published electronically: February 6, 2012
- Additional Notes: The authors were supported by the Research Project MSM 0021620839 from the Czech Ministry of Education
The first author was additionally supported in part by grant GAAV IAA 100190901
The second author was partly supported by grant GAČR 201/07/0388. - Communicated by: Thomas Schlumprecht
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3435-3444
- MSC (2010): Primary 46B20, 46B25
- DOI: https://doi.org/10.1090/S0002-9939-2012-11175-X
- MathSciNet review: 2929012