On real Cartan factors

被引:49
作者
Kaup, W
机构
[1] Universität Tübingen,Mathematisches Institut
关键词
D O I
10.1007/BF02678189
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
JBW*-triples can be described (module 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 factor 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 LOGS [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.
引用
收藏
页码:191 / 222
页数:32
相关论文
共 26 条
[1]  
[Anonymous], 1977, MATH LECT
[2]  
[Anonymous], THEORY OPERATOR ALGE
[3]   WEAK STAR-CONTINUITY OF JORDAN TRIPLE PRODUCTS AND ITS APPLICATIONS [J].
BARTON, T ;
TIMONEY, RM .
MATHEMATICA SCANDINAVICA, 1986, 59 (02) :177-191
[4]   BOUNDED DERIVATIONS OF JB-TRIPLES [J].
BARTON, TJ ;
FRIEDMAN, Y .
QUARTERLY JOURNAL OF MATHEMATICS, 1990, 41 (163) :255-268
[5]  
Braun H., 1966, JORDAN ALGEBREN
[6]   HOLOMORPHIC CHARACTERIZATION OF JORDAN CSTAR-ALGEBRAS [J].
BRAUN, R ;
KAUP, W ;
UPMEIER, H .
MATHEMATISCHE ZEITSCHRIFT, 1978, 161 (03) :277-290
[7]  
CHU CH, 1993, J LOND MATH SOC, V47, P97
[8]   REAL ISOMETRIES BETWEEN JB-ASTERISK-TRIPLES [J].
DANG, T .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 114 (04) :971-980
[9]   THE GELFAND-NAIMARK THEOREM FOR JB-STAR-TRIPLES [J].
FRIEDMAN, Y ;
RUSSO, B .
DUKE MATHEMATICAL JOURNAL, 1986, 53 (01) :139-148
[10]  
HANCHEOLSEN H, 1984, MONOGRAPHS STUD MATH, V21