This is an announcement for the paper "On quantification of weak sequential completeness" by O.F.K. Kalenda, H. Pfitzner and J. Spurny.
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.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 9 pages
Submitted from: kalenda@karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.6553
or