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 $D\geq 1$ and $q\geq 3$ be two integers. $H(D)=H(D,q)$ denote the $D$-dimensional Hamming graph over a $q$-element set. ${\mathcal T}(D)$ Terwilliger algebra of $H(D)$. $V(D)$ standard T}(D)$-module. $\omega$ complex scalar. We consider unital associative $\mathfrak K_\omega$ defined by generators relations. The are $A$ $B$. relations $A^2 B-2 ABA +B A^2 =B+\omega A$, $B^2A-2 BAB+AB^2=A+\om...

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert bases, and of reconstruction of the frames by projections and other bounded module operators with suitable ranges. We...

Kečkić and Lazović introduced an axiomatic approach to Fredholm theory by considering type elements in a unital $$C^{*}$$ -algebra as generalization of -Fredholm operators on the standard Hilbert -module Mishchenko Fomenko properly infinite von Neumann algebra Breuer. In this paper, we establish semi-Fredholm -algebras continuation Lazović. We introduce notion element semi-Weyl -algebra. prove ...

We study Ore extensions of non-unital associative rings. provide a characterization simple differential polynomial rings $R[x;\delta ]$, under the hypothesis that $R$ is $s$-unital and $\ker (\delta )$ contains non-zero idempotent. This

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 A and B be separable C∗-algebras, A unital and B stable. It is shown that there is a natural six-terms exact sequence which relates the group which arises by considering all semi-split extensions of A by B to the group which arises by restricting the attention to unital semi-split extensions of A by B. The six-terms exact sequence is an unpublished result of G. Skandalis. Let A,B be separab...

let r be a ring, m a right r-module and (s,≤) a strictly ordered monoid. in this paper we will show that if (s,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ s, then the module [[ms,≤]] of generalized power series is a uniserial right [[rs,≤]] ]]-module if and only if m is a simple right r-module and s is a chain monoid.