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Continuous linear operators on C(K, X) and pointwise weakly precompact subsets of C(K, X)

Published online by Cambridge University Press:  24 October 2008

A. lger
A. lger
Affiliation:
Department of Mathematics, Bogazici University, 80815 Bebek, Istanbul, Turkey
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Abstract

Let K be a compact Hausdorif space, X a Banach space and C(K, X) the Banach space of all continuous functions : KX equipped with the supremum norm. A subset H of C(K, X) is pointwise weakly precompact if, for each t in K, the set Ht) = {(t):H} is weakly precompact. In this note we study the images of a bounded pointwise weakly precompact subset H of C(K, X) under several classes of linear operators on C(K, X).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 1 , January 1992 , pp. 143 - 150
Copyright
Copyright © Cambridge Philosophical Society 1992

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