Isometries between groups of invertible elements in $C^{*}$-algebras
Volume 209 / 2012
Studia Mathematica 209 (2012), 103-106
MSC: Primary 46L05; Secondary 46B04.
DOI: 10.4064/sm209-2-1
Abstract
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.
