Isometric Jordan isomorphisms of group algebras. (English) Zbl 07908375
Summary: 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.
MSC:
| 43A20 | \(L^1\)-algebras on groups, semigroups, etc. |
Keywords:
locally compact group; group algebra; isometric isomorphism; isometric Jordan isomorphism; local isometric automorphism; approximately local isometric automorphismReferences:
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