Weak compactness in Köthe-Bochner spaces and regular methods of summability

• Autorzy: Nowak M.
• Języki publikacji: EN

Abstrakty

EN

Let (E, || · ||_E) be a Banach function space, and let (X, || · ||_X) be a Banach space. Let. E(X)_ñ stand for the order continuous dual of a Köthe-Bochner space E(X) (i.e. E(X)_ñ consists of all linear functionals F on E(X) such that for a net (ƒ_σ) in E(X), || ƒ_σ (·) ||x [formula] in E implies F(ƒ_σ) → 0). We present a characterization of conditionally σ (E(X), E(X)_ñ)-compact and relatively σ (E(X), E(X)_ñ) compact subsets of E(X) in terms of regular methods of summability. We generalize S. Diaz's criteria for conditional weak compactness and relative weak compactness in L¹ (X).

Słowa kluczowe

EN

conditional weak compactness; Köthe-Bochner spaces; regular methods of summability; relative weak compactness

PL

przestrzeń Köthe-Bochnera; regularna metoda sumowalności; warunek słabej zwartości; względna słaba zwartość

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 4
• Strony: 417--425
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Nowak M.

• Institute of Mathematics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

Bibliografia

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