Isometries between groups of invertible elements in Banach algebras

2009/04/14 by Osamu Hatori, Hatori, Osamu
Mathematics · #46B04 #47B48 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B04 #msc:47B48

paper · pdf · doi:10.48550/arxiv.0904.2074

13pages

arxiv created 2009/04/14 · arxiv updated 2009/12/01

Abstract

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)^-1T is an isometrical group isomorphism. In particular, T(1)^-1T is extended to an isometrical real algebra isomorphism from A onto B.

Related

• Linear extensions of isometries between groups of invertible elements in Banach algebras
• An algebraic property of an isometry between the groups of invertible elements in Banach algebras
• Isometries between groups of invertible elements in C^*-algebras
• Isometries between groups of invertible elements in Fourier-Stieltjes algebras
• On the structure of Banach algebras associated with automorphisms