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Paper's Title:

Unital Compact Homomorphisms Between Extended Analytic Uniform Algebras


D. Alimohammadi and M. Mayghani

Department of Mathematics,
Faculty of Science, Arak University,
PO Box 38156-8-8349, Arak,


Let X and K be compact plane sets with KX. We denote by A(X,K) and A(X) the algebras of all continuous complex-valued functions on X which are analytic on int(K) and int(X), respectively. It is known that A(X,K) and A(X) are natural uniform algebras on X. A(X) and A(X,K) are called analytic uniform algebra and extended analytic uniform algebra on X, respectively. In this paper we study unital homomorphisms between extended analytic uniform algebras and investigate necessary and sufficient conditions for which these homomorphisms to be compact. We also determine the spectrum of unital compact endomorphisms of extended analytic uniform algebras.

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