Weak sequential completeness and compactness in topological function spaces

• Autorzy: Nowak M.
• Języki publikacji: EN

Abstrakty

EN

Let (E, r) be a Hausdorff locally convex-solid function space (over a cr-finite measure space) and let E* stand for its topological dual. It is proved that the space (E, r) is weakly sequentially complete if and only if r is a c-Lebesgue and cr-Levy topology. In particular, a characterization of weak sequential completeness of Or-licz spaces L* in terms of Orlicz functions is given. Moreover, it is proved that the Eberlein-Smulian type theorem remains valid for a locally convex space (E, o~(E, E*)). A characterization of conditional and relative weak compactness in (E, r) is obtained.

Słowa kluczowe

EN

function space; Orlicz space; locally solid topologies; Lebesgue topologies; Levy topologies; weak sequential completeness; conditional weak compactness; weak compactness

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr spec.
• Strony: 155--165
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Nowak M.

• Faculty of Mathematics, Informatics and Econometrics, University of Zielona Góra, ul. Szafrana 4A, 65-516 Zielona Góra, Poland,

Bibliografia

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Uwagi

Dedicated to Professor Julian Musielak on his 75th birthday.