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arXiv · 1208.6337

Closed Unitary and Similarity Orbits of Normal Operators in Purely Infinite C*-Algebras

Paul Skoufranis
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Abstract

We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are approximately unitarily equivalent in said algebras with trivial K_1-group. Some upper and lower bounds for the distance between unitary orbits will be obtained based on these methods. In addition, a complete characterization of when one normal operator is in the closed similarity orbit of another normal operator will be given for unital, simple, purely infinite C*-algebras and type III factors with separable predual.

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Paul Skoufranis. 2012-11-29. Closed Unitary and Similarity Orbits of Normal Operators in Purely Infinite C*-Algebras. https://doi.org/10.1016/j.jfa.2013.04.009

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