Bulletin of the Belgian Mathematical Society - Simon Stevin

Zero products preserving maps from the Fourier algebra of amenable groups

Jafar Soltani Farsani

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 11 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1407765887

Digital Object Identifier
doi:10.36045/bbms/1407765887

Mathematical Reviews number (MathSciNet)
MR3250776

Zentralblatt MATH identifier
1314.47055

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

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

Citation

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


Export citation