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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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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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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DOI: https://doi.org/10.1007/s00025-024-02244-x
Keywords
- Locally compact group
- group algebra
- isometric isomorphism
- isometric Jordan isomorphism
- local isometric automorphism
- approximately local isometric automorphism