Spherical isometries of finite dimensional C^⁎-algebras

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• 作者：Ryotaro Tanaka¹ ; ^{r-tanaka@math.kyushu-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; ^{ryotarotanaka@m.sc.niigata-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Isometries ; Unit sphere ; Unitary group ; Faces ; Jordan isomorphisms
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：337-341
• 全文大小：259 K

文摘

In this paper, it is shown that every surjective isometry between the unit spheres of two finite dimensional C^⁎$C^{⁎}$-algebras extends to a real-linear Jordan ⁎-isomorphism followed by multiplication operator by a fixed unitary element. This gives an affirmative answer to Tingley's problem between two finite-dimensional C^⁎$C^{⁎}$-algebras. Moreover, we show that if two finite dimensional C^⁎$C^{⁎}$-algebras have isometric unit spheres, then they are ⁎-isomorphic.