We determine the extreme points of the set of graph traces of norm one for any finite graph E satisfying Condition (K). We also describe an application to the space of tracial states on the graph C∗-algebra.

In this paper we study the problem of when the corona algebra of a non-unital C∗-algebra is purely infinite. A complete answer is obtained for stabilisations of simple and unital algebras that have enough comparison of positive elements. Our result relates the pure infiniteness condition (from its strongest to weakest forms) to the geometry of the tracial simplex of the algebra, and to the beha...

ABSTRACT. Suppose M is a hyperfinite von Neumann algebra with a tracial state φ and {a1, . . . , an} is a set of self-adjoint generators for M. We calculate δ0(a1, . . . , an), the modified free entropy dimension of {a1, . . . , an}. Moreover we show that δ0(a1, . . . , an) depends only on M and φ. Consequently δ0(a1, . . . , an) is independent of the choice of generators for M . In the course ...

We give an explicit description of the tracial state simplex C ⁎ -algebra ( G ) arbitrary connected, second countable, locally compact, solvable group . show that every lifts from a abelianized group, and intersection kernels all states is proper ideal unless abelian. As consequence, connected nonabelian Lie cannot embed into simple unital AF-algebra.

In this paper two independent and unitarily invariant projection matrices P (N) and Q(N) are considered and the large deviation is proven for the eigenvalue density of all polynomials of them as the matrix size N converges to in nity. The result is formulated on the tracial state space TS(A) of the universal C -algebra A generated by two selfadjoint projections. The random pair (P (N); Q(N)) de...

Let C = C(X) be the unital C*-algebra of all continuous functions on a finite CW complex X and let A be a unital simple C*-algebra with tracial rank at most one. We show that two unital monomorphisms φ,ψ : C → A are asymptotically unitarily equivalent, i.e., there exists a continuous path of unitaries {ut : t ∈ [0, 1)} ⊂ A such that lim t→1 utφ(f)ut = ψ(f) for all f ∈ C(X),

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 ...

λ(s)δt = δst and ρ(s)δt = δts−1 for s, t ∈ Γ. The reduced group C∗-algebra C∗ λΓ is the C∗-algebra generated by λ, likewise for C∗ ρΓ; C∗ λΓ = λ(CΓ) ‖ ‖ ⊂ B(`2Γ) and C∗ ρΓ = ρ(CΓ) ‖ ‖ ⊂ B(`2Γ). The group von Neumann algebra LΓ is the von Neumann algebra generated by λ; LΓ = λ(CΓ)′′ = ρ(CΓ)′. We sometime use M instead of LΓ, and L2M instead of `2Γ. We denote by τ the canonical tracial state on L...

We initiate a study of linear maps on Mn(C) that have the property they factor through tracial von Neumann algebra (A,τ) via operators Z∈Mn(A) whose entries consist positive elements from von-Neumann algebra. These often arise in context non-local games especially synchronous case. establish connection with convex sets Rn containing self-dual cones and existence these maps. The Choi matrix map ...