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Centralizers of Fourier algebra of an amenable group

Author: P. F. Renaud
Journal: Proc. Amer. Math. Soc. 32 (1972), 539-542
MSC: Primary 43A10
MathSciNet review: 0293019
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Abstract: Let G be a locally compact group with Fourier algebra $ A(G)$. We prove that if G is amenable then every centralizer of $ A(G)$ is determined by multiplication with an element of the Fourier-Stieltjes algebra of G. This result is then used to show that isometric centralizers correspond to characters of G.

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Keywords: Locally compact group, amenable group, Fourier algebra, centralizer
Article copyright: © Copyright 1972 American Mathematical Society

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