Bulletin of the Belgian Mathematical Society - Simon Stevin

Zero products preserving maps from the Fourier algebra of amenable groups

Jafar Soltani Farsani

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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.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 3 (2014), 523-534.

First available in Project Euclid: 11 August 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B48: Operators on Banach algebras
Secondary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.

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


Farsani, Jafar Soltani. Zero products preserving maps from the Fourier algebra of amenable groups. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 3, 523--534. doi:10.36045/bbms/1407765887. https://projecteuclid.org/euclid.bbms/1407765887

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