群代数的等距约旦同构

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-07-30 DOI:10.1007/s00025-024-02244-x

J. Alaminos, J. Extremera, C. Godoy, A. R. Villena

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引用次数: 0

摘要

让 G 和 H 都是局部紧凑群。我们将证明，每个收缩约旦同构（Phi :L^1(G)\rightarrow L^1(H)）要么是等距同构，要么是等距反同构。我们将应用这一结果来研究群集上的等距双面零积预器，并进一步研究群集的局部和近似局部等距自变量。

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Isometric Jordan Isomorphisms of Group Algebras

Let G and H be locally compact groups. We will show that each contractive Jordan isomorphism \(\Phi :L^1(G)\rightarrow L^1(H)\) is either an isometric isomorphism or an isometric anti-isomorphism. We will apply this result to study isometric two-sided zero product preservers on group algebras and, further, to study local and approximately local isometric automorphisms of group algebras.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.