Article ID Journal Published Year Pages File Type
4589847 Journal of Functional Analysis 2016 42 Pages PDF
Abstract

In this paper, we study closed convex hulls of unitary orbits in various C⁎C⁎-algebras. For unital C⁎C⁎-algebras with real rank zero and a faithful tracial state determining equivalence of projections, a notion of majorization describes the closed convex hulls of unitary orbits for self-adjoint operators. Other notions of majorization are examined in these C⁎C⁎-algebras. Combining these ideas with the Dixmier property, we demonstrate unital, infinite dimensional C⁎C⁎-algebras of real rank zero and strict comparison of projections with respect to a faithful tracial state must be simple and have a unique tracial state. Also, closed convex hulls of unitary orbits of self-adjoint operators are fully described in unital, simple, purely infinite C⁎C⁎-algebras.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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