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Search: All articles in the CJM digital archive with keyword real rank zero

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1. CJM Online first

Ng, P. W.; Skoufranis, P.
Closed convex hulls of unitary orbits in certain simple real rank zero C$^*$-algebras
In this paper, we characterize the closures of convex hulls of unitary orbits of self-adjoint operators in unital, separable, simple C$^*$-algebras with non-trivial tracial simplex, real rank zero, stable rank one, and strict comparison of projections with respect to tracial states. In addition, an upper bound for the number of unitary conjugates in a convex combination needed to approximate a self-adjoint are obtained.

Keywords:convex hull of unitary orbits, real rank zero C*-algebras simple, eigenvalue function, majorization
Category:46L05

2. CJM 2001 (vol 53 pp. 592)

Perera, Francesc
Ideal Structure of Multiplier Algebras of Simple $C^*$-algebras With Real Rank Zero
We give a description of the monoid of Murray-von Neumann equivalence classes of projections for multiplier algebras of a wide class of $\sigma$-unital simple $C^\ast$-algebras $A$ with real rank zero and stable rank one. The lattice of ideals of this monoid, which is known to be crucial for understanding the ideal structure of the multiplier algebra $\mul$, is therefore analyzed. In important cases it is shown that, if $A$ has finite scale then the quotient of $\mul$ modulo any closed ideal $I$ that properly contains $A$ has stable rank one. The intricacy of the ideal structure of $\mul$ is reflected in the fact that $\mul$ can have uncountably many different quotients, each one having uncountably many closed ideals forming a chain with respect to inclusion.

Keywords:$C^\ast$-algebra, multiplier algebra, real rank zero, stable rank, refinement monoid
Categories:46L05, 46L80, 06F05

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