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arXiv · 2407.00489

Isometric Jordan isomorphisms of group algebras

J. Alaminos·J. Extremera·C. Godoy·A. R. Villena
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Abstract

Let $G$ and $H$ be locally compact groups. We will show that each contractive Jordan isomorphism $\Phi\colon L^1(G)\to L^1(H)$ 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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J. Alaminos, J. Extremera, C. Godoy, A. R. Villena. 2024-06-29. Isometric Jordan isomorphisms of group algebras. https://arxiv.org/abs/2407.00489

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