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.

引用

页码：233 / 241

页数：9

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SEPARABLE C*-ALGEBRAS AND WEAK* FIXED POINT PROPERTY

SEPARABLE C-ALGEBRAS AND WEAK FIXED POINT PROPERTY