Publication: Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras
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KU Authors
Co-Authors
Kaniuth, Eberhard
Lau, Anthony To-Ming
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Embargo Status
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Abstract
Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism phi : A -> B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and phi) axe given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms from A into A with closed range. Our results are applied to Fourier algebras of locally compact groups.
Source
Publisher
Institute of Mathematics of the Polish Academy of Sciences
Subject
Mathematics
Citation
Has Part
Source
Studia Mathematica
Book Series Title
Edition
DOI
10.4064/sm183-1-3