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Weakly precompact operators on C b ( X , E ) with the strict topology

Juliusz Stochmal — 2016

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

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