Compact homomorphisms between algebras of analytic functions

Richard Aron; Pablo Galindo; Mikael Lindström

ArticleOriginal scientific text

Title

Compact homomorphisms between algebras of analytic functions

Authors ¹, ², ³

Affiliations

Department of Mathematics, Kent State University, Kent, Ohio 44242, U.S.A.
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjasot, Valencia, Spain
Department of Mathematics, Åbo Akademi University, FIN-20500 Åbo, Finland

Abstract

We prove that every weakly compact multiplicative linear continuous map from

H^{\infty} (D)

into

H^{\infty} (D)

is compact. We also give an example which shows that this is not generally true for uniform algebras. Finally, we characterize the spectra of compact composition operators acting on the uniform algebra

H^{\infty} (B_{E})

, where

B_{E}

is the open unit ball of an infinite-dimensional Banach space E.

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Title

Compact homomorphisms between algebras of analytic functions

Affiliations

Abstract

Bibliography