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arXiv · 2302.00931

Linear preservers on idempotents of Fourier algebras

Ying-Fen Lin·Shiho Oi
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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.

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Ying-Fen Lin, Shiho Oi. 2023-02-02. Linear preservers on idempotents of Fourier algebras. https://arxiv.org/abs/2302.00931

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