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Isometric Jordan Isomorphisms of Group Algebras

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Abstract

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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Funding

The authors were supported by MCIN/AEI/10.13039/501100011033 and “ERDF A way of making Europe” Grant PID2021-122126NB-C31 and by Junta de Andalucía Grant FQM185.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain

    J. Alaminos, J. Extremera & A. R. Villena

  2. Departamento de Matemáticas, Universidad de Alicante, Crta. San Vicente del Raspeig s/n, San Vicente del Raspeig, Alicante, Spain

    C. Godoy

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  1. J. Alaminos
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  2. J. Extremera
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  3. C. Godoy
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  4. A. R. Villena
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Contributions

All authors contributed equally to the study conception and design. All authors read and approved the final manuscript.

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Correspondence to A. R. Villena.

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Alaminos, J., Extremera, J., Godoy, C. et al. Isometric Jordan Isomorphisms of Group Algebras. Results Math 79, 213 (2024). https://doi.org/10.1007/s00025-024-02244-x

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