傅立叶代数幂等元的线性保持器

IF 0.5 4区数学 Q3 MATHEMATICS Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-02-02 DOI:10.4153/s0008439523000395

Ying-Fen Lin, Shiho Oi

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引用次数: 0

摘要

本文给出了在局部紧群的傅立叶代数上保持幂等元的有界复线性算子的一个表示。当这样的算子是正的或收缩的时，我们证明了该算子是由连续群同态或连续群反同态诱导的。如果群是完全不连通的，则傅立叶代数上的有界同态可以通过幂等保持算子来实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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LINEAR PRESERVERS ON IDEMPOTENTS OF FOURIER ALGEBRAS

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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来源期刊

Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

24 months

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