Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Multipliers and asymptotic behaviour of the Fourier algebra of nonamenable groups


Author: Claudio Nebbia
Journal: Proc. Amer. Math. Soc. 84 (1982), 549-554
MSC: Primary 43A07; Secondary 43A30
DOI: https://doi.org/10.1090/S0002-9939-1982-0643747-3
MathSciNet review: 643747
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a locally compact group and $ A(G)$ the algebra of matrix coefficients of the regular representation. We prove that $ G$ is amenable if and only if there exist functions $ u \in A(G)$ which vanish at infinity at any arbitrarily slow rate. The "only if" part of the result was essentially known. With the additional hypothesis that $ G$ be discrete, we deduce that $ G$ is amenable if and only if every multiplier of the algebra $ A(G)$ is a linear combination of positive definite functions. Again, the "only if" part of this result was known.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A07, 43A30

Retrieve articles in all journals with MSC: 43A07, 43A30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0643747-3
Keywords: Locally compact group, amenable group, multiplier of the Fourier algebra, Fourier-Stieltjes algebra, asymptotic behaviour of coefficients of the regular representation
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society