Weakly compact homomorphisms between small algebras of analytic functions

Pablo Galindo; Mikael Lindström

doi:10.1112/S0024609301008402

Weakly compact homomorphisms between small algebras of analytic functions

Pablo Galindo^*, Mikael Lindström

^*Corresponding author for this work

Mathematics

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

5 Citations (Scopus)

Abstract

The weak compactness of the composition operator C_Φ,(f) = f o Φ acting on the uniform algebra of analytic uniformly continuous functions on the unit ball of a Banach space with the approximation property is characterized in terms of Φ. The relationship between weak compactness and compactness of these composition operators and general homomorphisms is also discussed.

Original language	English
Pages (from-to)	715-726
Number of pages	12
Journal	Bulletin of the London Mathematical Society
Volume	33
Issue number	6
DOIs	https://doi.org/10.1112/S0024609301008402
Publication status	Published - Nov 2001
MoE publication type	A1 Journal article-refereed

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title = "Weakly compact homomorphisms between small algebras of analytic functions",

abstract = "The weak compactness of the composition operator CΦ,(f) = f o Φ acting on the uniform algebra of analytic uniformly continuous functions on the unit ball of a Banach space with the approximation property is characterized in terms of Φ. The relationship between weak compactness and compactness of these composition operators and general homomorphisms is also discussed.",

author = "Pablo Galindo and Mikael Lindstr{\"o}m",

note = "Funding Information: Research of the rst author partially supported by DGES (Spain) pr. 96-0758; research of the second author supported by the Academy of Finland.",

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AU - Lindström, Mikael

N1 - Funding Information: Research of the rst author partially supported by DGES (Spain) pr. 96-0758; research of the second author supported by the Academy of Finland.

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N2 - The weak compactness of the composition operator CΦ,(f) = f o Φ acting on the uniform algebra of analytic uniformly continuous functions on the unit ball of a Banach space with the approximation property is characterized in terms of Φ. The relationship between weak compactness and compactness of these composition operators and general homomorphisms is also discussed.

AB - The weak compactness of the composition operator CΦ,(f) = f o Φ acting on the uniform algebra of analytic uniformly continuous functions on the unit ball of a Banach space with the approximation property is characterized in terms of Φ. The relationship between weak compactness and compactness of these composition operators and general homomorphisms is also discussed.

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U2 - 10.1112/S0024609301008402

DO - 10.1112/S0024609301008402

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VL - 33

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JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 6

ER -

Weakly compact homomorphisms between small algebras of analytic functions

Abstract

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