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 |
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Pages (from-to) | 383-405 |
Journal | International Journal of Mathematics |
Volume | 8 |
DOIs | |
Publication status | Published - 1 Jan 1997 |