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June 1988 Compact Weighted Composition Operators on Function Algebras
Hiroyuki TAKAGI
Tokyo J. Math. 11(1): 119-129 (June 1988). DOI: 10.3836/tjm/1270134266


A weighted endomorphism of an algebra is an endomorphism followed by a multiplier. In [6] and [4], H. Kamowitz characterized compact weighted endomorphisms of $C(X)$ and the disc algebra. In this note we define a weighted composition operator on a function algebra as a generalization of a weighted endomorphism, and characterize compact weighted composition operators on a function algebra satisfying a certain condition [Theorem 2]. This theorem not only includes Kamowitz's results as corollaries, but also has an application to compact weighted composition operators on the Hardy class $H^\infty(D)$.


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Hiroyuki TAKAGI. "Compact Weighted Composition Operators on Function Algebras." Tokyo J. Math. 11 (1) 119 - 129, June 1988.


Published: June 1988
First available in Project Euclid: 1 April 2010

zbMATH: 0663.47021
MathSciNet: MR947951
Digital Object Identifier: 10.3836/tjm/1270134266

Rights: Copyright © 1988 Publication Committee for the Tokyo Journal of Mathematics


Vol.11 • No. 1 • June 1988
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