manuscripta mathematica

, Volume 61, Issue 3, pp 297–314

Jordan axioms for C*-algebras


  • Angel Rodríguez Palacios
    • Departamento de Análisis MatemáticoUniversidad de Granada

DOI: 10.1007/BF01258441

Cite this article as:
Rodríguez Palacios, A. Manuscripta Math (1988) 61: 297. doi:10.1007/BF01258441


A complex Banach spaceA which is also an associative algebra provided with a conjugate linear vector space involution * satisfying (a2)*=(a*)2, ∥aa*a∥=∥a3 and ∥ab+ba∥≦2a∥∥b∥ for alla, b inA is shown to be a C*-algebra. The assumptions onA can be expressed in terms of the Jordan algebra obtained by symmetrization of the product ofA and are satisfied by any C*-algebra. Thus we obtain a purely Jordan characterization of C*-algebras.

Copyright information

© Springer-Verlag 1988