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C* -Algebras of Real Rank Zero Whose K0's are not Riesz Groups

Published online by Cambridge University Press:  20 November 2018

K. R. Goodearl
K. R. Goodearl*
Affiliation:
Department of Mathematics, University of California Santa Barbara, California 93106, U.S.A., e-mail: goodearl@math.ucsb.edu
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Abstract

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Examples are constructed of stably finite, imitai, separable C* -algebras A of real rank zero such that the partially ordered abelian groups K0(A) do not satisfy the Riesz decomposition property. This contrasts with the result of Zhang that projections in C* -algebras of real rank zero satisfy Riesz decomposition. The construction method also produces a stably finite, unital, separable C* -algebra of real rank zero which has the same K-theory as an approximately finite dimensional C*-algebra, but is not itself approximately finite dimensional.

Keywords

46L8019K14
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 429 - 437
Copyright
Copyright © Canadian Mathematical Society 1996

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