An algebraic property of an isometry between the groups of invertible elements in Banach algebras

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dc.creatorHatori, Osamu
dc.date2009-04-20
dc.date.accessioned2026-07-07T13:05:54Z
dc.date.available2026-07-07T13:05:54Z
dc.descriptionWe show that if $T$ is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then $T$ is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the underling algebras are closed unital standard operator algebras, $(T(e_A))^{-1}T$ is extended to a surjective real algebra isomorphism; if $T$ is a surjective isometry from the invertible group of a unital commutative Banach algebra onto that of a unital semisimple Banach algebra, then $(T(e_A))^{-1}T$ is extended to a surjective isometrical real algebra isomorphism between the two underling algebras.
dc.description13pages
dc.identifierhttps://arxiv.org/abs/0904.2940
dc.identifierhttp://arxiv.org/abs/0904.2940
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227639
dc.subjectFunctional Analysis
dc.subject47B48,46B04
dc.titleAn algebraic property of an isometry between the groups of invertible elements in Banach algebras
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