DISCRETIZATION OF C*-ALGEBRAS

被引：2

作者：

Heunen, Chris ^{[1
]}

Reyes, Manuel L. ^{[2
]}

机构：

[1] Univ Edinburgh, Sch Informat, Edinburgh EH8 9AB, Midlothian, Scotland

[2] Bowdoin Coll, Dept Math, Brunswick, ME 04011 USA

来源：

JOURNAL OF OPERATOR THEORY | 2017年 / 77卷 / 01期

基金：

英国工程与自然科学研究理事会; 美国国家科学基金会;

关键词：

Noncommutative topology; noncommutative set; function algebra; discrete space; profinite completion; pure state; diffuse measure; spectrum obstruction; EXTENSIONS;

D O I：

10.7900/jot.2015jun16.2109

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate how a C*-algebra could consist of functions on a noncommutative set: a discretization of a C*-algebra A is a *-homomorphism A -> M that factors through the canonical inclusion C (X) * subset of l(infinity) (X) when restricted to a commutative C*-subalgebra. Any C*-algebra admits an injective but nonfunctorial discretization, as well as a possibly noninjective functorial discretization, where M is a C*-algebra. Any subhomogenous C*-algebra admits an injective functorial discretization, where M is a W*-algebra. However, any functorial discretization, where M is an AW*-algebra, must trivialize A = B(H) for any infinite-dimensional Hilbert space H.

引用

页码：19 / 37

页数：19

共 39 条

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[2]

AKEMANN CA, 1971, PAC J MATH, V39, P1

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