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 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 l(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.

Keywords

• Weakly sequentially complete Banach space
• Schur property
• quantitative versions of weak sequential completeness
• quantitative versions of the Schur property
• L-embedded Banach space