The Dixmier property and tracial states for C⁎-algebras
نویسندگان
چکیده
منابع مشابه
Local tracial C*-algebras
Let $Omega$ be a class of unital $C^*$-algebras. We introduce the notion of a local tracial $Omega$-algebra. Let $A$ be an $alpha$-simple unital local tracial $Omega$-algebra. Suppose that $alpha:Gto $Aut($A$) is an action of a finite group $G$ on $A$ which has a certain non-simple tracial Rokhlin property. Then the crossed product algebra $C^*(G,A,alpha)$ is a unital local traci...
متن کاملThe Tracial Rokhlin Property for Actions of Finite Groups on C*-algebras
We define “tracial” analogs of the Rokhlin property for actions of finite groups, approximate representability of actions of finite abelian groups, and of approximate innerness. We prove the following four analogs of related “nontracial” results. • The crossed product of an infinite dimensional simple separable unital C*-algebra with tracial rank zero by an action of a finite group with the tra...
متن کاملTracial Rokhlin property for automorphisms on simple AT-algebras
Let A be a unital simple AT-algebra of real rank zero. Given an isomorphism γ1 : K1(A)→ K1(A), we show that there is an automorphism α : A → A such that α∗1 = γ1 which has the tracial Rokhlin property. Consequently, the crossed product A ⋊α Z is a simple unital AH-algebra with real rank zero. We also show that automorphism with Rokhlin property can be constructed from minimal homeomorphisms on ...
متن کاملlocal tracial c*-algebras
let $omega$ be a class of unital $c^*$-algebras. we introduce the notion of a local tracial $omega$-algebra. let $a$ be an $alpha$-simple unital local tracial $omega$-algebra. suppose that $alpha:gto $aut($a$) is an action of a finite group $g$ on $a$ which has a certain non-simple tracial rokhlin property. then the crossed product algebra $c^*(g,a,alpha)$ is a unital local traci...
متن کاملDixmier Approximation and Symmetric Amenability for C ∗ - Algebras
We study some general properties of tracial C∗-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C∗-algebras. In the second part, we consider continuous bundles of tracial von Neumann algebras and classify some of them.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2017
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2017.06.026