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

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.

arXiv commentThe second version of this paper completely removes the technical constraints in Theorem 4.2 of the first version due to the existence of a paper due to Dadarlat. The results in the second section of this paper provide an alternate proof of specific subcases of Dadarlat's result

References in corpus (2)

• Approximate Homotopy of Homomorphisms from $C(X)$ into a Simple $C^{\ast }$-algebra
• Normal Limits of Nilpotents in C*-Algebras

Cited by in corpus (2)

• Closed Convex Hulls of Unitary Orbits in C${}^{\ast }$-Algebras of Real Rank Zero
• Normal Limits of Nilpotents in C*-Algebras