In this paper, we extend the notion of generalized tracial approximation to non-unital case. An example approximation, which comes from dynamical systems, is also provided. We use machinery Cuntz subequivalence work in setting.

Let C be a unital AH-algebra and A be a unital simple C∗-algebra with tracial rank zero. It has been shown that two unital monomorphisms φ, ψ : C → A are approximately unitarily equivalent if and only if [φ] = [ψ] in KL(C,A) and τ ◦ φ = τ ◦ ψ for all τ ∈ T (A), where T (A) is the tracial state space of A. In this paper we prove the following: Given κ ∈ KL(C,A) with κ(K0(C)+\{0}) ⊂ K0(A)+\{0} an...

Let X be an infinite compact metric space with finite covering dimension and let h : X → X be a minimal homeomorphism. We show that the associated crossed product C*-algebra A = C∗(Z, X, h) has tracial rank zero whenever the image of K0(A) in Aff(T (A)) is dense. As a consequence, we show that these crossed product C*-algebras are in fact simple AH algebras with real rank zero. When X is connec...

ABSTRACT. The subject of this paper are polynomials in multiple non-commuting variables. For polynomials of this type orthogonal with respect to a state, we prove a Favardtype recursion relation. On the other hand, free Sheffer polynomials are a polynomial family in non-commuting variables with a resolvent-type generating function. Among such families, we describe the ones that are orthogonal. ...

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.

We construct an algebra with twisted commutation relations and equip it with the shift. For appropriate irregularity of the non-local commutation relations we prove that the tracial state is the only translation-invariant state.

Given two orthogonal projections $$\{P,Q\}$$ in a non commutative tracial probability space, we prove relations between the moments of $$P+Q$$ , commutator $$i(PQ-QP)$$ and $$P+QPQ$$ those angle operator PQP. Our proofs are purely algebraic enumerative does not assume P, Q satisfying Voiculescu’s freeness property or being general position. As far as sum concerned, obtained follow from binomial...

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 ...

Boundary integral equations and Nyström discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weaklysingular kernel arises, in which case specialized quadratures that modify the matrix entries near the diagonal are needed to reach a high accuracy. We describe the construction of four different quadratures which handle logarith...