Compact homomorphisms between algebras of analytic functions

Richard Aron; Pablo Galindo; Mikael Lindström

Compact homomorphisms between algebras of analytic functions

Richard Aron^*, Pablo Galindo, Mikael Lindström

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

34 Citations (Scopus)

Abstract

We prove that every weakly compact multiplicative linear continuous map from H^∞(D) into H^∞(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^∞(B_E), where B_E is the open unit ball of an infinite-dimensional Banach space E.

Original language	English
Pages (from-to)	235-247
Number of pages	13
Journal	Studia Mathematica
Volume	123
Issue number	3
Publication status	Published - 1997
MoE publication type	A1 Journal article-refereed

Cite this

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abstract = "We prove that every weakly compact multiplicative linear continuous map from H∞(D) into H∞(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∞(BE), where BE is the open unit ball of an infinite-dimensional Banach space E.",

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AU - Lindström, Mikael

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AB - We prove that every weakly compact multiplicative linear continuous map from H∞(D) into H∞(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∞(BE), where BE is the open unit ball of an infinite-dimensional Banach space E.

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JO - Studia Mathematica

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Compact homomorphisms between algebras of analytic functions

Abstract

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