Isometries between groups of invertible elements in Banach algebras

Details Isometries between groups of invertible elements in Banach algebras Isometries between groups of invertible elements in Banach algebras

2009-04-14

arxiv.org/abs/0904.2074v1

Mathematics

Functional Analysis

13pages

Scientific paper

We show that if $T$ is an isometry (as metric spaces) from an open subgroup of the group of the invertible elements in a unital semisimple commutative Banach algebra onto an open subgroup of the group of the invertible elements in a unital Banach algebra, then $T(1)^{-1}T$ is an isometrical group isomorphism. In particular, $T(1)^{-1}T$ is extended to an isometrical real algebra isomorphism from $A$ onto $B$.

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