Quasidiagonal traces on exact $C^\ast$-algebras
作者： James Gabe
DOI:
关键词: Class (set theory) 、 Separable space 、 Trace (linear algebra) 、 Combinatorics 、 Mathematics
摘要: Recently, it was proved by Tikuisis, White and Winter that any faithful trace on a separable, nuclear $C^\ast$-algebras in the UCT class is quasidiagonal. Building their work, we generalise result, show faithful, amenable exact We also prove exact, quasidiagonal $C^\ast$-algebra
arxiv.org参考文章(14)
James Gabe, Efren Ruiz, Absorbing representations with respect to closed operator convex cones arXiv: Operator Algebras. ,(2015)
Joachim Zacharias, Wilhelm Winter, Completely positive maps of order zero arXiv: Operator Algebras. ,(2009)
MARIUS DADARLAT, MORPHISMS OF SIMPLE TRACIALLY AF ALGEBRAS International Journal of Mathematics. ,vol. 15, pp. 919- 957 ,(2004) , 10.1142/S0129167X04002636
Dan Voiculescu, A note on quasi-diagonal C*-algebras and homotopy Duke Mathematical Journal. ,vol. 62, pp. 267- 271 ,(1991) , 10.1215/S0012-7094-91-06211-3
Marius Dadarlat, Quasidiagonal Morphisms and Homotopy Journal of Functional Analysis. ,vol. 151, pp. 213- 233 ,(1997) , 10.1006/JFAN.1997.3145
E. Kirchberg, On Subalgebras of the Car-Algebra Journal of Functional Analysis. ,vol. 129, pp. 35- 63 ,(1995) , 10.1006/JFAN.1995.1041
Jonathan Rosenberg, Claude Schochet, The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized $K$-functor Duke Mathematical Journal. ,vol. 55, pp. 431- 474 ,(1987) , 10.1215/S0012-7094-87-05524-4
Eberhard Kirchberg, C*-Nuclearity implies CPAP Mathematische Nachrichten. ,vol. 76, pp. 203- 212 ,(1977) , 10.1002/MANA.19770760115
Huaxin Lin, Zhuang Niu, Guihua Gong, Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras arXiv: Operator Algebras. ,(2014)
Aaron Tikuisis, Stuart White, Wilhelm Winter, Quasidiagonality of nuclear C*-algebras arXiv: Operator Algebras. ,(2015) , 10.4007/ANNALS.2017.185.1.4