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Certain Properties of $K_0$-monoids Preserved by Tracial Approximation
  Published:2011-09-22
 Printed: Jun 2013
Canadian Mathematical Bulletin
  • Qingzhai Fan,
    Department of Mathematics, Shanghai Maritime University, 1550 Haigang Ave., New Harbor City, Shanghai 201306, China
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Abstract

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 $TA\Omega$: (1) weak comparability, (2) strictly unperforated, (3) strictly cancellative.
Keywords: $C^*$-algebra, tracial approximation, $K_0$-monoid $C^*$-algebra, tracial approximation, $K_0$-monoid
MSC Classifications: 46L05, 46L80, 46L35 show english descriptions General theory of $C^*$-algebras
$K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
Classifications of $C^*$-algebras 46L05 - General theory of $C^*$-algebras
46L80 - $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
46L35 - Classifications of $C^*$-algebras
 
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