Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 21, Number 3 (2014), 523-534.
Zero products preserving maps from the Fourier algebra of amenable groups
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.
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 3 (2014), 523-534.
First available in Project Euclid: 11 August 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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