Open Access
august 2014 Zero products preserving maps from the Fourier algebra of amenable groups
Jafar Soltani Farsani
Bull. Belg. Math. Soc. Simon Stevin 21(3): 523-534 (august 2014). DOI: 10.36045/bbms/1407765887

Abstract

Let $G$ be a locally compact amenable group. The goal of this paper is to investigate the problem of surjective zero products preserving maps from the Fourier algebra of $G$ into a completely contractive Banach algebra. We show that if $B$ is a completely contractive Banach algebra which is faithful and factors weakly, then every surjective completely bounded linear map from $A(G)$ into $B$ which preserves zero products is a weighted homomorphism. Moreover an equivalent condition is given for such a map to be a homomorphism. In particular, this result implies that if $B$ is a commutative C$^*$-algebra or a matrix space and $T:A(G)\rightarrow B$ is a continuous surjective linear map which preserves zero products, then $T$ is a weighted homomorphism and there is an equivalent condition for $T$ to be a homomorphism.

Citation

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Jafar Soltani Farsani. "Zero products preserving maps from the Fourier algebra of amenable groups." Bull. Belg. Math. Soc. Simon Stevin 21 (3) 523 - 534, august 2014. https://doi.org/10.36045/bbms/1407765887

Information

Published: august 2014
First available in Project Euclid: 11 August 2014

zbMATH: 1314.47055
MathSciNet: MR3250776
Digital Object Identifier: 10.36045/bbms/1407765887

Subjects:
Primary: 47B48
Secondary: 43A30

Keywords: ‎amenable group , Fourier algebra , locally compact group , operator spaces , ‎set of spectral synthesis ‎ , Weighted homomorphism

Rights: Copyright © 2014 The Belgian Mathematical Society

Vol.21 • No. 3 • august 2014
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