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The Structure of Positive Elements for C*-Algebras with Real Rank Zero

    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 of S(A) is a Riesz group, and lattice-ordered under some additional assumptions on A.

    Partially supported by MEC-DGICYT grant no. PB95-0626, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya.

    Dedicat al Juanje i la Neus, en ser pares.