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

Francesc Perera

doi:https://doi.org/10.1142/S0129167X97000196

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

Francesc Perera

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

16 Citations (Scopus)

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 language	English
Pages (from-to)	383-405
Journal	International Journal of Mathematics
Volume	8
DOIs	https://doi.org/10.1142/S0129167X97000196
Publication status	Published - 1 Jan 1997

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Perera, F. (1997). The structure of positive elements for C*-algebras with real rank zero. International Journal of Mathematics, 8, 383-405. https://doi.org/10.1142/S0129167X97000196

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AB - 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.

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