On weak drop property and quasi-weak drop property

• Autorzy: J. H. Qiu
• Języki publikacji: EN

Abstrakty

EN

Every weakly sequentially compact convex set in a locally convex space has the weak drop property and every weakly compact convex set has the quasi-weak drop property. An example shows that the quasi-weak drop property is strictly weaker than the weak drop property for closed bounded convex sets in locally convex spaces (even when the spaces are quasi-complete). For closed bounded convex subsets of quasi-complete locally convex spaces, the quasi-weak drop property is equivalent to weak compactness. However, for closed bounded convex sets in sequentially complete locally convex spaces, even the weak drop property does not imply weak compactness. A quasi-complete locally convex space is semi-reflexive if and only if its closed bounded convex subsets have the quasi-weak drop property. For strong duals of quasi-barrelled spaces, semi-reflexivity is equivalent to every closed bounded convex set having the quasi-weak drop property. From this, reflexivity of a quasi-complete, quasi-barrelled space (in particular, a Fréchet space) is characterized by the quasi-weak drop property of the space and of the strong dual.

Kategorie tematyczne

• 46A55: Convex sets in topological linear spaces; Choquet theory
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 156
• Numer: 2
• Strony: 189-202

Daty

wydano

2003

Twórcy

autor

J. H. Qiu

• Department of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, People's Republic of China

Identyfikatory

DOI

10.4064/sm156-2-8