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Centralizers of the Fourier Algebra of an Amenable Group

P. F. Renaud
Proceedings of the American Mathematical Society
Vol. 32, No. 2 (Apr., 1972), pp. 539-542
DOI: 10.2307/2037854
Stable URL: http://www.jstor.org/stable/2037854
Page Count: 4
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Centralizers of the Fourier Algebra of an Amenable Group
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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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