Abstract
JBW*-triples can be described (modulo W*-algebras, compare [13]) by those of type I. Among these the (complex) Cartan factors are the building blocks. We determine for every complex Cartan factorU all conjugations of the underlying complex Banach space and hence all real forms (in the sense of [15]) ofU, calledreal Cartan factors. We also give a concrete list of all isomorphy classes of real Cartan factors which generalizes the classification of LOOS [23] to infinite dimensions. Furthermore, we give an explicit description of the full automorphism group as well as the group of all surjective ℝ-linear isometries for every non-exceptional real Cartan factor and decide which of the real or complex Cartan factors are isometrically equivalent to each other as real Banach spaces.
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Kaup, W. On real cartan factors. Manuscripta Math 92, 191–222 (1997). https://doi.org/10.1007/BF02678189
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DOI: https://doi.org/10.1007/BF02678189