Geodesic
Isometries between groups of invertible elements in $C^{*}$-algebras
Osamu Hatori 1   ; Keiichi Watanabe 1
1 Department of Mathematics Faculty of Science Niigata University 950-2181 Niigata, Japan
Studia Mathematica, Tome 209 (2012) no. 2, pp. 103-106 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We describe all surjective isometries between open subgroups of the groups of invertible elements in unital $C^{*}$-algebras. As a consequence the two $C^{*}$-algebras are Jordan $*$-isomorphic if and only if the groups of invertible elements in those $C^{*}$-algebras are isometric as metric spaces.
DOI : 10.4064/sm209-2-1
Keywords: describe surjective isometries between subgroups groups invertible elements unital * algebras consequence * algebras jordan * isomorphic only groups invertible elements those * algebras isometric metric spaces

Osamu Hatori  1   ; Keiichi Watanabe  1

1 Department of Mathematics Faculty of Science Niigata University 950-2181 Niigata, Japan 
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Osamu Hatori; Keiichi Watanabe. Isometries between groups of invertible elements
 in $C^{*}$-algebras. Studia Mathematica, Tome 209 (2012) no. 2, pp. 103-106. doi: 10.4064/sm209-2-1

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