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Periodica Mathematica Hungarica

, Volume 72, Issue 2, pp 248–251 | Cite as

On a characterization of commutativity for \(C^*\)-algebras via gyrogroup operations

  • Toshikazu Abe
  • Osamu Hatori
Article

Abstract

We show that a unital \(C^*\)-algebra is commutative if and only if the gyrogroup of the set of positive invertible elements is in fact a group.

Keywords

Gyrocommutative gyrogroup Positive invertible element  \(C^*\)-algebra Commutativity 

Mathematics Subject Classification

46L05 20N05 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.Department of Mathematical Science, Graduate School of Science and TechnologyNiigata UniversityNiigataJapan
  2. 2.Department of Mathematics, Faculty of ScienceNiigata UniversityNiigataJapan

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