On approximation of homomorphisms of algebras of entire functions on Banach spaces

H. M. Pryimak

Abstract


It is known due to R. Aron, B. Cole and T. Gamelin that every complex homomorphism of the algebra of entire functions of bounded type on a Banach space $X$ can be approximated in some sens by a net of point valued homomorphism. In this paper we consider the question about a generalization of this result for the case of homomorphisms to any commutative Banach algebra $A.$ We obtained some positive results if $A$ is the algebra of uniformly continuous analytic functions on the unit ball of $X.$

Keywords


analytic functions on Banach space, homomorphisms of algebras of analytic functions, approximation property

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