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arXiv · 1608.04350

Majorization in C*-algebras

Ping Wong Ng·Leonel Robert·Paul Skoufranis
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Abstract

We investigate the closed convex hull of unitary orbits of selfadjoint elements in arbitrary unital C*-algebras. Using a notion of majorization against unbounded traces, a characterization of these closed convex hulls is obtained. Furthermore, for C*-algebras satisfying Blackadar's strict comparison of positive elements by traces or for collections of C*-algebras with a uniform bound on their nuclear dimension, an upper bound for the number of unitary conjugates in a convex combination required to approximate an element in the closed convex hull within a given error is shown to exist. This property, however, fails for certain "badly behaved" simple nuclear C*-algebras.

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Ping Wong Ng, Leonel Robert, Paul Skoufranis. 2016-08-15. Majorization in C*-algebras. https://arxiv.org/abs/1608.04350

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