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Journal of Operator Theory

Volume 69, Issue 2, Spring 2013  pp. 535-543.

$K_0$-monoid properties preserved by tracial approximation

Authors Qingzhai Fan
Author institution: Department of Mathematics, Shanghai Maritime University, 1550 Haigang Ave. in New Harbor City, Shanghai 201306, China

Summary:  We show that the following $K_0$-monoid properties of $C^*$-algebras in the class $\Omega$ are inherited by simple unital $C^*$-algebras in the class $TA\Omega$: \nr{i} almost unperforated, \nr{ii} $n$-comparison, \nr{iii} cancellation property, \nr{iv} Riesz decomposition property.

Keywords:  $C^*$-algebra, tracial approximation, $K_0$-monoid

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