Weakly precompact operators on $C_{b}(X,E)$ with the strict topology

Stochmal, Juliusz

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 1, pp. 65-77.

Résumé

Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let C_b(X,E) be the space of all E-valued bounded continuous functions on X, equipped with the strict topology β. We study weakly precompact operators T:C_b(X,E) → F. In particular, we show that if X is a paracompact k-space and E contains no isomorphic copy of l¹, then every strongly bounded operator T:C_b(X,E) → F is weakly precompact.

Détail

Keywords: spaces of vector-valued continuous functions, strict topologies, operator measures, strongly bounded operators, weakly precompact operators

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