Comparison Properties of the Cuntz Semigroup and Applications to C*-algebras

被引：3

作者：

Bosa, Joan ^{[1
]}

Petzka, Henning ^{[2
,3
]}

机构：

[1] Univ Glasgow, Sch Math & Stat, 15 Univ Gardens, Glasgow G12 8QW, Lanark, Scotland

[2] Fraunhofer Inst Intelligent Anal & Informat Syst, D-53757 St Augustin, Germany

[3] Univ Bonn, Rhein Friedrich Wilhelms Univ Bonn, Inst Informat 3, Romerstr 164, D-53117 Bonn, Germany

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2018年 / 70卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

classification of C*-algebras; cuntz semigroup; CORONA FACTORIZATION PROPERTY; DIMENSION FUNCTIONS; ELLIOTT CONJECTURE; REFINEMENT MONOIDS; CLASSIFICATION; THEOREM; TRACES;

D O I：

10.4153/CJM-2016-049-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study comparison properties in the category Cu aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the corona factorization property (CFP) and omega-comparison. We show differences of all properties by providing examples that suggest that the corona factorization for C*-algebras might allow for both finite and infinite projections. In addition, we show that Rordam's simple, nuclear C*-algebra with a finite and an infinite projection does not have the CFP.

引用

页码：26 / 52

页数：27

共 33 条

[1] [Anonymous], 1986, MATH SURVEYS MONOGR
[2] Antoine R., MEM AM MATH IN PRESS
[3] Geometric structure of dimension functions of certain continuous fields
Antoine, Ramon
Bosa, Joan
Perera, Francesc
Petzka, Henning
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (04) : 2403 - 2423
[4] COMPLETIONS OF MONOIDS WITH APPLICATIONS TO THE CUNTZ SEMIGROUP
Antoine, Ramon
Bosa, Joan
Perera, Francesc
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2011, 22 (06) : 837 - 861
[5] Refinement monoids with weak comparability and applications to regular rings and C-*-algebras
Ara, P
Pardo, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (03) : 715 - 720
[6] Ara P, 2011, CONTEMP MATH, V534, P1
[7] EXTENDING STATES ON PREORDERED SEMIGROUPS AND THE EXISTENCE OF QUASI-TRACES ON C-ASTERISK-ALGEBRAS
BLACKADAR, B
RORDAM, M
[J]. JOURNAL OF ALGEBRA, 1992, 152 (01) : 240 - 247
[8] Blackadar B, 1998, K-theory for operator algebras, volume 5 of Mathematical Sciences Research Institute Publications, V5
[9] AN ALGEBRAIC APPROACH TO THE RADIUS OF COMPARISON
Blackadar, Bruce
Robert, Leonel
Tikuisis, Aaron P.
Toms, Andrew S.
Winter, Wilhelm
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (07) : 3657 - 3674
[10] The Cuntz semigroup, the Elliott conjecture, and dimension functions on C *-algebras
Brown, Nathanial P.
Perera, Francesc
Toms, Andrew S.
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2008, 621 : 191 - 211

← 1 2 3 4 →