Classification of homomorphisms from C(X) to simple C*-algebras of real rank zero

被引:15
作者
Gong, GH [1 ]
Lin, HX
机构
[1] Univ Puerto Rico, Dept Math, Rio Piedras, PR 00931 USA
[2] Univ Oregon, Dept Math, Eugene, OR 97403 USA
[3] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China
来源
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2000年 / 16卷 / 02期
关键词
simple C*-algebras; real rank zero; K-theory; tracial states; almost multiplicative maps;
D O I
10.1007/s101140050001
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let A be a unital simple C*-algebra of real rank zero, stable rank one, with weakly unperforated K-o(A) and unique normalized quasi-trace tau, and let X be a compact metric space. We show that two monomorphisms phi, psi : C(X) --> A are approximately unitarily equivalent ii, and only if phi and psi, induce the same element in KL(C(X), A) and the two linear functionals tau o phi and tau o psi, are equal. We also show that, with an injectivity condition, an almost multiplicative morphism from C(X) into A with vanishing KK-obstacle is close to a homomorphism.
引用
收藏
页码:181 / 206
页数:26
相关论文
共 50 条
[31]   REAL RANK ZERO FOR PURELY INFINITE CORONA ALGEBRAS [J].
Ng, Ping Wong .
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2022, 52 (01) :243-261
[32]   Homomorphisms of C*-Algebras and Their K-theory [J].
Naderi, Parastoo ;
Rooin, Jamal .
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2022, 48 (02) :465-478
[33]   Homomorphisms of C*-Algebras and Their K-theory [J].
Parastoo Naderi ;
Jamal Rooin .
Bulletin of the Iranian Mathematical Society, 2022, 48 :465-478
[34]   APPROXIMATE UNITARY EQUIVALENCE IN SIMPLE C*-ALGEBRAS OF TRACIAL RANK ONE [J].
Lin, Huaxin .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (04) :2021-2086
[35]   DETERMINANT RANK OF C*-ALGEBRAS [J].
Gong, Guihua ;
Lin, Huaxin ;
Xue, Yifeng .
PACIFIC JOURNAL OF MATHEMATICS, 2015, 274 (02) :405-436
[36]   LIMITS AND C*-ALGEBRAS OF LOW RANK OR DIMENSION [J].
Brown, Lawrence G. ;
Pedersen, Gert K. .
JOURNAL OF OPERATOR THEORY, 2009, 61 (02) :381-417
[37]   Asymptotic unitary equivalence and classification of simple amenable C*-algebras [J].
Lin, Huaxin .
INVENTIONES MATHEMATICAE, 2011, 183 (02) :385-450
[38]   Asymptotic unitary equivalence and classification of simple amenable C∗-algebras [J].
Huaxin Lin .
Inventiones mathematicae, 2011, 183 :385-450
[39]   Kishimoto’s Conjugacy Theorems in Simple C*-Algebras of Tracial Rank One [J].
Huaxin Lin .
Integral Equations and Operator Theory, 2015, 83 :95-150
[40]   Classification of O∞-Stable C∗-Algebras [J].
Gabe, James .
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 293 (1461) :1-115