Open projections and suprema in the Cuntz semigroup

被引：2
|
作者：
Bosa, Joan [1 ]
Tornetta, Gabriele [1 ]
Zacharias, Joachim [1 ]
机构：
[1] Univ Glasgow, Sch Math & Stat, 15 Univ Gardens, Glasgow G12 8QW, Lanark, Scotland
来源：
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2018年 / 164卷 / 01期
基金：
英国工程与自然科学研究理事会;
关键词：
C-ASTERISK-ALGEBRAS; DIMENSION FUNCTIONS; STAR-ALGEBRAS;
D O I：
10.1017/S030500411600089X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We provide a new and concise proof of the existence of suprema in the Cuntz semigroup using the open projection picture of the Cuntz semigroup initiated in [12]. Our argument is based on the observation that the supremum of a countable set of open projections in the bidual of a C*-algebra A is again open and corresponds to the generated hereditary C*-subalgebra of A.
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页码：135 / 146
页数：12
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