J Austral Math Soc Ser A 45 pp303--319, 1988.

Composition Operators on Weighted Spaces of Continuous Functions

R. K. Singh and W. H. Summers

(Received 27 February 1987)

Abstract

We give algebraic criteria for distinguishing composition operators among all continuous linear operators on spaces of continuous functions with topologies generated by seminorms that are weighted analogues of the supremum norm. In another direction, we also characterize those self maps of the underlying topological space which induce composition operators on such weighted spaces, as well as determine conditions on these self maps which correspond to various basic properties of the induced composition operator. Our results are applied to a question concerning translation invariance which arises in the context of topological dynamics.

1980 AMS Subject Classification (1985 Revision): 47B38

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Authors

R. K. Singh: Department of Mathematics, University of Jammu, Jammu-180 001, India.
W. H. Summers: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, U.S.A.

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Last Modified: Wed Feb 19 10:27:48 2003