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).File in questo prodotto:
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