Weak sequential compactness and completeness in Koethe-Bochner spaces

• Autorzy: Nowak M.
• Języki publikacji: EN

Abstrakty

EN

Let (E,[...]) be a Banach function space over a probability measure space, and let (X,[...]) be a Banach space. Let E(X)[...] stand for the order continuous dual of a Koethe-Bochner space E(X ) (i.e., E(X )[...] consists of all linear functionals F on E(X ) such that for a net (f[sigma]) in E(X),[...] 0 in E implies F(f[sigma]) --> 0). We present a characterization of conditional sigma(E(X), E(X)[...])-compactness and relative sigma(E(X), E(X)[...] )-compactness in E(X ). We generalize J. Diestel, W. Ruess and W. Schachermayer's criterion for relative weak compactness in E(X ) as well as M. Talagrand's results on conditional weak compactness and weak sequential completeness in E(X ) by removing order continuity of (E, [...]). Applications to Orlicz-Bochner spaces are given.

Słowa kluczowe

EN

conditional weak compactness; Koethe-Bochner spaces; relative weak compactness; sequential weak completeness

PL

analiza funkcjonalna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 3
• Strony: 209--220
• Opis fizyczny: Bibliogr. 25 poz.,

Twórcy

autor

Nowak M.

• Institute of Mathematics, T. Kotarbiński Pedagogical University, Pl. Słowiański 9, 65-069 Zielona Góra, Poland