SEPARABLE C*-ALGEBRAS AND WEAK* FIXED POINT PROPERTY

被引：0
|
作者：
Fendler, Gero [1 ]
Leinert, Michael [2 ]
机构：
[1] Univ Vienna, Fac Math, A-1090 Vienna, Austria
[2] Heidelberg Univ, Inst Angew Math, D-69120 Heidelberg, Germany
来源：
PROBABILITY AND MATHEMATICAL STATISTICS-POLAND | 2013年 / 33卷 / 02期
关键词：
Weak* fixed point property; discrete dual; UKK*; BANACH-SPACES; NONEXPANSIVE-MAPPINGS; CENTERS; THEOREM;
D O I：
暂无
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We show that the spectrum (A) over cap of a separable C*-algebra A is discrete if and only if A*, the Banach space dual of A, has the weak* fixed point property. We prove further that these properties are equivalent among others to the uniform weak* Kadec-Klee property of A* and to the coincidence of the weak* topology with the norm topology on the pure states of A. If one assumes the set-theoretic diamond axiom, then the separability is necessary.
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页码：233 / 241
页数：9
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