Unitary equivalence of automorphisms of separable C*-algebras

Abstract

We prove that the automorphisms of any separable C*-algebra that does not have continuous trace are not classifiable by countable structures up to unitary equivalence. This implies a dichotomy for the Borel complexity of the relation of unitary equivalence of automorphisms of a separable unital C*-algebra: Such relation is either smooth or not even classifiable by countable structures.

Submitted for publication

References in corpus (5)

• Z-stability of crossed products by strongly outer actions II
• Classification of outer actions of Z^N on O_2
• A simple C*-algebra with finite nuclear dimension which is not Z-stable
• Z^N-actions on UHF algebras of infinite type
• Classification of uniformly outer actions of Z^2 on UHF algebras

Cited by in corpus (5)

• Logic and operator algebras
• Conjugacy and cocycle conjugacy of automorphisms of ${\mathcal{O}}_2$ are not Borel
• Definable $\mathrm{K}$-homology of separable C*-algebras
• Classification problems from the descriptive set theoretical perspective
• Borel equivalence relations in the space of bounded operators