Publication:
Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras

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Kaniuth, Eberhard
Lau, Anthony To-Ming

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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.

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Institute of Mathematics of the Polish Academy of Sciences

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Mathematics

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Studia Mathematica

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10.4064/sm183-1-3

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