Spherical isometries of finite dimensional C-algebras

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Abstract

In this paper, it is shown that every surjective isometry between the unit spheres of two finite dimensional 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-algebras. Moreover, we show that if two finite dimensional C-algebras have isometric unit spheres, then they are ⁎-isomorphic.

Original languageEnglish
Pages (from-to)337-341
Number of pages5
JournalJournal of Mathematical Analysis and Applications
Volume445
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

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Keywords

  • Faces
  • Isometries
  • Jordan isomorphisms
  • Unit sphere
  • Unitary group

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