2014
DOI: 10.1016/j.aim.2014.05.022
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Unitary equivalence of automorphisms of separable C*-algebras

Abstract: 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. IntroductionIf A is a separable C*-algebra, the group Aut(A) of automorphisms of A is a Polish group with respect to… Show more

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Cited by 12 publications
(14 citation statements)
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“…This consequence is proved using different methods in [25], in much greater generality (for separable C*-algebras which do not have continuous trace).…”
Section: Shift Automorphisms and The Existence Of A Dense Turbulent Omentioning
confidence: 99%
“…This consequence is proved using different methods in [25], in much greater generality (for separable C*-algebras which do not have continuous trace).…”
Section: Shift Automorphisms and The Existence Of A Dense Turbulent Omentioning
confidence: 99%
“…Moreover, each of these is known to be not classifiable by countable structures; this is evident for c 0 /ℓ p by Example 3.2, and can be shown for [0,1] N /c 0 and [0, 1] N /ℓ p using Lemma 3.1 of [14]. In fact, we have the following, part (a) of which is essentially due to Oliver [16]:…”
Section: Examples and Restrictions Of Turbulent Actionsmentioning
confidence: 82%
“…A prototypical example of turbulent group action is the action of ℓ 1 on R N by translation. A standard argument allows one to deduce the following nonclassification criterion from turbulence of the action ℓ 1 R N and Hjorth's turbulence theorem [H2, Theorem 3.18]; see for example [L,Lemma 3.2 and Criterion 3.3].…”
Section: Suppose That Gmentioning
confidence: 99%