Automatic continuity of biorthogonality preservers between weakly compact $JB^*$-triples and atomic $JBW^*$-triples

Volume 204 / 2011

María Burgos, Jorge J. Garcés, Antonio M. Peralta Studia Mathematica 204 (2011), 97-121 MSC: Primary 46L05, 46L70; Secondary 17A40, 17C65, 46K70, 46L40, 47B47, 47B49. DOI: 10.4064/sm204-2-1

Abstract

We prove that every biorthogonality preserving linear surjection from a weakly compact $JB^*$-triple containing no infinite-dimensional rank-one summands onto another $JB^*$-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic $JBW^*$-triples containing no infinite-dimensional rank-one summands is automatically continuous. Consequently, two atomic $JBW^*$-triples containing no rank-one summands are isomorphic if and only if there exists a (not necessarily continuous) biorthogonality preserving linear surjection between them.

Authors

  • María BurgosDepartamento de Análisis Matemático
    Facultad de Ciencias
    Universidad de Granada
    18071 Granada, Spain
    e-mail
  • Jorge J. GarcésDepartamento de Análisis Matemático
    Facultad de Ciencias
    Universidad de Granada
    18071 Granada, Spain
    e-mail
  • Antonio M. PeraltaDepartamento de Análisis Matemático
    Facultad de Ciencias
    Universidad de Granada
    18071 Granada, Spain
    e-mail

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