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

Abstract

Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(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: Cb(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: Cb(X,E)→ F is weakly precompact.

Authors and Affiliations

Juliusz Stochmal

Keywords

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  • EP ID EP472965
  • DOI 10.7151/dmdico.1182
  • Views 72
  • Downloads 0

How To Cite

Juliusz Stochmal (2016). Weakly precompact operators on Cb(X,E) with the strict topology. Discussiones Mathematicae Differential Inclusions Control and Optimization, 36(1), 65-77. https://europub.co.uk/articles/-A-472965