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Weak Continuity of a Composition Map Between Spaces of Compact Operators and Banach Valued Continuous Functions

Published online by Cambridge University Press:  20 November 2018

Rajappa K. Asthagiri
Rajappa K. Asthagiri*
Affiliation:
Miami University Middletown, OH 45042
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Abstract

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This paper characterizes the Banach space E for the sequential continuity and the continuity on bounded sets of the composition map m: C(S, E)wk x K{E,F)wk —> C(S,F)wk. Here, K(E,F) denotes the Banach space of compact linear operators on the Banach space E to the Banach space F with the usual operator norm, and for any Banach space E, Ewk denote the Banach space E with the weak topology. Also we denote by C(S, E) the Banach space of E valued continuous functions on a nonvoid compact Hausdorff space S with sup norm.

Keywords

46B9946E1546E4047B05.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 2 , 01 June 1991 , pp. 145 - 146
Copyright
Copyright © Canadian Mathematical Society 1991

References

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