Geodesic
Isometries between groups of invertible elements in Banach algebras
Osamu Hatori1
1Department of Mathematics Faculty of Science Niigata University Niigata 950-2181 Japan
Studia Mathematica, Tome 194 (2009) no. 3, pp. 293-304
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We show that if $T$ is an isometry (as metric spaces) from an open subgroup of the group of invertible elements in a unital semisimple commutative Banach algebra $A$ onto a open subgroup of the group of invertible elements in a unital Banach algebra $B$, then $T(1)^{-1}T$ is an isometrical group isomorphism. In particular, $T(1)^{-1}T$ extends to an isometrical real algebra isomorphism from $A$ onto $B$.
DOI : 10.4064/sm194-3-5
Keywords: isometry metric spaces subgroup group invertible elements unital semisimple commutative banach algebra subgroup group invertible elements unital banach algebra isometrical group isomorphism particular extends isometrical real algebra isomorphism

Osamu Hatori  1

1 Department of Mathematics Faculty of Science Niigata University Niigata 950-2181 Japan 
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Osamu Hatori. Isometries between groups of invertible
 elements in Banach algebras. Studia Mathematica, Tome 194 (2009) no. 3, pp. 293-304. doi: 10.4064/sm194-3-5

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