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, Volume 86, Issue 1, pp 311–335 | Cite as

On real forms of JB*-triples

  • José M. Isidro
  • W. Kaup
  • Angel Rodríguez Palacios
Article

Abstract

We introduce real JB*-triples as real forms of (complex) JB*-triples and give an algebraic characterization of surjective linear isometries between them. As main result we show: A bijective (not necessarily continuous) linear mapping between two real JB*-triples is an isometry if and only if it commutes with the cube mappinga→a 3={aaa}. This generalizes a result of Dang for complex JB*-triples. We also associate to every tripotent (i.e. fixed point of the cube mapping) and hence in particular to every extreme point of the unit ball in a real JB*-triple numerical invariants that are respected by surjective linear isometries.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • José M. Isidro
    • 1
  • W. Kaup
    • 2
  • Angel Rodríguez Palacios
    • 3
  1. 1.Facultad de MatemáticasUniversidad de SantiagoSantiago de CompostelaSpain
  2. 2.Mathematisches InstitutUniversität TübingenTübingenGermany
  3. 3.Dep. Analisis Matematico Facultad de CienciasUniversidad de GranadaGranadaSpain

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