Mathematische Annalen

, Volume 330, Issue 1, pp 45–58

Relatively weakly open sets in closed balls of Banach spaces, and real JB*-triples of finite rank

  • Julio Becerra Guerrero
  • Ginés López Pérez
  • Antonio M. Peralta
  • A Rodríguez-Palacios
Article

DOI: 10.1007/s00208-004-0537-y

Cite this article as:
Guerrero, J., Pérez, G., Peralta, A. et al. Math. Ann. (2004) 330: 45. doi:10.1007/s00208-004-0537-y

Abstract.

We prove that, given a real JB*-triple X, there exists a nonempty relatively weakly open subset of the closed unit ball of X with diameter less than 2 (if and) only if the Banach space of X is isomorphic to a Hilbert space. Moreover we give the structure of real JB*-triples whose Banach spaces are isomorphic to Hilbert spaces. Such real JB*-triples are also characterized in two different purely algebraic ways.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Julio Becerra Guerrero
    • 1
  • Ginés López Pérez
    • 2
  • Antonio M. Peralta
    • 2
  • A Rodríguez-Palacios
    • 2
  1. 1.Universidad de GranadaFacultad de CienciasGranadaSpain
  2. 2.Universidad de GranadaFacultad de CienciasGranadaSpain