In this paper, we extend the constructions of Boava and Exel to present C∗-algebra associated with an injective endomorphism a group finite cokernel as partial algebra consequently crossed product. With representation, another way study such C∗-algebras, only using tools from products.

Using various finite dimensional approximation properties, four convex subsets of the tracial space of a unital C∗-algebra are defined. One subset is characterized by Connes’ hypertrace condition. Another is characterized by hyperfiniteness of GNS representations. The other two sets are more mysterious but are shown to be intimately related to Elliott’s classification program. Applications of t...

In this paper, the norm attaining operators in Frechet spaces are considered. These characterized based on their density, normality, linearity and compactness. It is shown that image dense for a normal injective operator space, as well its inverse given self-adjoint. A space also to be if adjoint attains condition under which attainability normality of an coincides given. Furthermore, between l...

It is well-known that a countably injective module is Σ-injective. In Proc. Amer. Math. Soc. 316, 10 (2008), 3461-3466, Beidar, Jain and Srivastava extended it and showed that an injective module M is Σ-injective if and only if each essential extension of M(א0) is a direct sum of injective modules. This paper extends and simplifies this result further and shows that an injective module M is Σ-i...

We prove that if a non-singular planar map $\Lambda \in C^2(\mathbb R^2,\mathbb R^2)$ has convex component, then it is injective. do not assume strict convexity.

‎let $m$ be a non-zero finitely generated module over a commutative noetherian local ring $(r,mathfrak{m})$ with $dim_r(m)=t$‎. ‎let $i$ be an ideal of $r$ with $grade(i,m)=c$‎. ‎in this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎the main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎tor^{r}_c(k,h^c_i(m))to kotim...

Given a collection C of subsets of a finite set X, let S C = ∪S∈CS. Philip Hall’s celebrated theorem [2] concerning ‘systems of distinct representatives’ tells us that for any collection C of subsets of X there exists an injective (i.e. one-to-one) function f : C → X with f(S) ∈ S for all S ∈ C if and and only if C satisfies the property that for all non-empty subsets C ′ of C we have | S C | ≥...

In this paper, we study injective and nuclear real W*- C*-algebras. The connection of these concepts with similar enveloping C*-algebras is considered. equivalence the injectivity nuclearity for shown. As a consequence, factors types II1, II, III1, III0 III (0 1) are completely described.

We prove that the crossed product C∗-algebra C∗ r (Γ, ∂Γ) of a free group Γ with its boundary ∂Γ naturally sits between the reduced group C∗algebra C∗ r Γ and its injective envelope I(C∗ r Γ). In other words, we have natural inclusion C∗ r Γ ⊂ C∗ r (Γ, ∂Γ) ⊂ I(C∗ r Γ) of C∗-algebras.