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

Authors:
O. F. K. Kalenda and J. Spurný

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

Published electronically:
February 6, 2012

MathSciNet review:
2929012

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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 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.

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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

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

DOI:
https://doi.org/10.1090/S0002-9939-2012-11175-X

Keywords:
Weakly sequentially complete Banach space,
Schur property,
quantitative versions of weak sequential completeness,
quantitative versions of the Schur property,
$L$-embedded Banach space

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

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.