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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Manuscripta Mathematica.
( Vol. 92 NO.2 / (1997))
On real Cartan factors
Wilhelm Kaup,
Pages. 191-222
Abstract $JBW^*$-triples can be described (modulo $W^*$-algebras, compare [13]
by those oftype I. Among these the (complex) Cartan factors are the building
blocks. We determine for every complex Cartan $U$ all conjugations of the
underlying complex Banach space and hence all real forms (in the sense of [15])
of $U$, called real 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 IR-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.
Contents 1. Introduction
2. $JB^*$-triples and real forms
3. Complex Cartan factors
4. Real Cartan factors
5. Automorphism groups and isometric equivalence
6. Some remarks
Key words
Mathmatical Subject Classification