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

摘要

We will investigate the norm closure of the unitary and similarity orbits ofnormal operators in unital, simple, purely infinite C*-algebras. An operatortheoretic proof will be given to the classification of when two normaloperators are approximately unitarily equivalent in said algebras with trivialK_1-group. Some upper and lower bounds for the distance between unitary orbitswill be obtained based on these methods. In addition, a completecharacterization of when one normal operator is in the closed similarity orbitof another normal operator will be given for unital, simple, purely infiniteC*-algebras and type III factors with separable predual.