Closed Convex Hulls of Unitary Orbits in C$^*$-Algebras of Real Rank Zero

Paul Skoufranis

doi:10.1016/j.jfa.2015.09.018

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arXiv · 1504.04825

Closed Convex Hulls of Unitary Orbits in C$^*$-Algebras of Real Rank Zero

Paul Skoufranis

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Abstract

In this paper, we study closed convex hulls of unitary orbits in various C$^*$-algebras. For unital 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$^*$-algebras. Combining these ideas with the Dixmier property, we demonstrate unital, infinite dimensional 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$^*$-algebras.

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BibTeX RIS

Paul Skoufranis. 2015-04-19. Closed Convex Hulls of Unitary Orbits in C$^*$-Algebras of Real Rank Zero. https://doi.org/10.1016/j.jfa.2015.09.018

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