The structure of positive elements for C*-algebras with real rank zero

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Abstract

In this paper we give a representation theorem for the Cuntz monoid S(A) of a σ-unital C*-algebra A with real rank zero and stable rank one, which allows to prove several Riesz decomposition properties on the monoid. As a consequence, it is proved that the comparability conditions (FCQ), stable (FCQ) and (FCQ+) are equivalent for simple C*-algebras with real rank zero. It is also shown that the Grothendieck group K*0(A) of S(A) is a Riesz group, and lattice-ordered under some additional assumptions on A.
Original languageEnglish
Pages (from-to)383-405
JournalInternational Journal of Mathematics
Volume8
DOIs
Publication statusPublished - 1 Jan 1997

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