Linear preservers on idempotents of Fourier algebras
Functional Analysis
2023-02-03 v1
Abstract
In this article, we give a representation of bounded complex linear operators which preserve idempotent elements on the Fourier algebra of a locally compact group. When such an operator is moreover positive or contractive, we show that the operator is induced by either a continuous group homomorphism or a continuous group anti-homomorphism. If the groups are totally disconnected, bounded homomorphisms on the Fourier algebra can be realised by the idempotent preserving operators.
Keywords
Cite
@article{arxiv.2302.00931,
title = {Linear preservers on idempotents of Fourier algebras},
author = {Ying-Fen Lin and Shiho Oi},
journal= {arXiv preprint arXiv:2302.00931},
year = {2023}
}
Comments
16pages