On quantification of weak sequential completeness

Ondrej Kalenda (1) , Hermann Pfitzner (2) , Jiri Spurny (1)

1 Department of Mathematical Analysis
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We consider several quantities related to weak sequential com- pleteness 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.

Mots clés: L-embedded Banach space; Weakly sequentially complete Banach space; Quantitative versions of weak sequential completeness; Quantitative versions of weak sequential completeness.

Domaines: Analyse fonctionnelle [math.FA]

Ondrej Kalenda, Hermann Pfitzner, Jiri Spurny. On quantification of weak sequential completeness. Journal of Functional Analysis, 2011, 260 (10), pp.2986-2996. ⟨hal-00544711⟩