Pure States on Free Group C*-Algebras

Abstract

Abstract.We prove that all the pure states of the reduced C

Classically Normal Pure States

“…6.7, where it is shown that C * (F R ) is nonseparable, but that every abelian subalgebra is separable. However, unlike the situation described in Corollary 0.9, we show in [7] that, if f is a pure state on C * (F R ), then A = {a ∈ C * (F R ) : f (a * a + aa * ) = 0} contains a sequential abelian approximate unit.…”

Unique expectations for discrete crossed products

“…Thanks to these efforts, we have various characterizations of the PEP, and know that it entails significant structural consequences for the inclusion. Very recently, several authors have advanced our understanding of the PEP for specific classes of inclusions [18,2,1,17,16]. This note continues the aforementioned line of inquiry, by characterizing (in terms of the dynamics) when the inclusion A ⊆ A ⋊ r G (resp.…”

“…if and only if for every non-zero irreducible representation π : A → B(H) and every T ∈ B(H), T π(a) = π(α(a))T, a ∈ A =⇒ T = 0. 1 We say that an action G A of a discrete group on a unital C * -algebra by * -automorphisms is free if αg ∈ Aut(A) has no non-zero dependent elements, for all e = g ∈ G. That is, if b ∈ A and ba = αg(a)b for all a ∈ A, then b = 0, unless g = e. 2 We say that G A is properly outer if for all e = g ∈ G, the only αg…”