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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

1. Aron, R. M. and Asthagiri, R. K., Weak Continuity of Mappings Between Spaces of Compact Operators, accepted for publication in Portugalia Mathematica.Google Scholar
2. Collins, H. S. and Ruess, W., Dual of Spaces of Operators, Studia Math 74 (1982), pp. 213–245.Google Scholar
3. Diestel, J. A., A Survey of the Results Related to the Dunford-Pettis Property, Contemporary Mathematics, 2, pp 15–60, A.M.S. publication, (1980).Google Scholar
4. Kalton, N. J., Spaces of Compact Operators, Math. Ann. 208, pp. 267–278 (1974).Google Scholar
5. Lewis, D. R., Conditional Weak Compactness in Certain Inductive Tensor Products, Math. Ann. 201, pp. 201–209(1973).Google Scholar
6. Rajappa, A. K., (Asthagiri, R. K.) Weak Continuity of Nonlinear Maps Between Banach Spaces, Dissertation, Kent State University, August, 1985.Google Scholar