Let X be a Banach space and X* its dual space. The classical Alaoglu theorem states that closed balls B-r* of X* are weak*-compact. Suppose now W*CC(X*) is the collection of all non-empty weak*-compact, convex subsets of X*. We shall define a certain weak*-topology T-w* on the hyperspace W*CC(X*). If X is separable, we shall prove that closed balls B-r* of W*CC(X*) are weak*-compact (T-w*-compact).

DE BLASI, F.s., Hu, T., Huang, J. (2009). Weak-topology and Alaoglu's theorem on hyperspace. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 10(1), 33-40.

Weak-topology and Alaoglu's theorem on hyperspace

DE BLASI, FRANCESCO SAVERIO;
2009-01-01

Abstract

Let X be a Banach space and X* its dual space. The classical Alaoglu theorem states that closed balls B-r* of X* are weak*-compact. Suppose now W*CC(X*) is the collection of all non-empty weak*-compact, convex subsets of X*. We shall define a certain weak*-topology T-w* on the hyperspace W*CC(X*). If X is separable, we shall prove that closed balls B-r* of W*CC(X*) are weak*-compact (T-w*-compact).
2009
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Weak-topology; Alaoglu theorem; weak-compactness; hyperspace
DE BLASI, F.s., Hu, T., Huang, J. (2009). Weak-topology and Alaoglu's theorem on hyperspace. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 10(1), 33-40.
DE BLASI, Fs; Hu, T; Huang, J
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/8068
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