Let Φ1, . . . ,Φn be strictly positive linear maps from a unital C∗algebra A into a C∗-algebra B and let Φ = ∑n i=1 Φi be unital. If f is an operator convex function on an interval J , then for every self-adjoint operator A ∈ A with spectrum contained in J , the following refinement of the Choi– Davis–Jensen inequality holds:

We show that the matricial norms of a non-unital operator algebra determine those of the algebra obtained by adjoining a unit to it. As applications , we classify two-dimensional unital operator algebras and show that the algebra of bounded holomorphic functions on a strongly pseudoconvex domain has a contractive representation that is not completely contractive.

‎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...

Let A be a Banach algebra. We call a pair (G,A) a Gelfand theory for A if the following axioms are satisfied: (G 1) A is a C∗-algebra, and G : A → A is a homomorphism; (G 2) the assignment L 7→ G−1(L) is a bijection between the sets of maximal modular left ideals of A and A, respectively; (G 3) for each maximal modular left ideal L of A, the linear map GL : A/G−1(L) → A/L induced by G has dense...

Let A be a Banach algebra, not necessarily unital, and let B be a closed subalgebra of A. We establish a connection between the Banach cyclic cohomology group HC(A) of A and the Banach B-relative cyclic cohomology group HCnB(A) of A. We prove that, for a Banach algebra A with a bounded approximate identity and an amenable closed subalgebra B of A, up to topological isomorphism, HC(A) = HCnB(A) ...

The common practice of slightly rewording the first paragraph or two of the introduction and calling it an abstract has always seemed a colossal waste of space to the author. Here, we will try to be as brief and to the point as possible. In this paper we prove the space of unital qubit channels is a Scott domain. We also provide a simple protocol to achieve Holevo capacity for these channels.

Let A be a unital commutative Banach algebra with maximal ideal space Max(A). We determine the rational H-type of GLn(A), the group of invertible n × n matrices with coefficients in A, in terms of the rational cohomology of Max(A). We also address an old problem of J. L. Taylor. Let Lcn(A) denote the space of “last columns” of GLn(A). We construct a natural isomorphism Ȟ(Max(A);Q) ∼= π2n−1−s(Lc...

By a theorem due to Kato and Ohtake, any (not necessarily strict) Morita context induces an equivalence between appropriate subcategories of the module categories of the two rings in the Morita context. These are in fact categories of firm modules for non-unital subrings. We apply this result to various Morita contexts associated to a comodule Σ of an A-coring C. This allows to extend (weak and...

We discuss the commutativity of certain rings with unity 1 and one-sided s-unital rings under each of the following conditions: xr[xs, y] = ±[x, yt]xn, xr[xs, y] = ±xn[x, yt], xr[xs, y] = ±[x, yt]ym, and xr[xs, y] = ±ym[x, yt], where r, n, and m are non-negative integers and t > 1, s are positive integers such that either s, t are relatively prime or s[x, y] = 0 implies [x, y] = 0. Further, we ...

By a theorem due to Kato and Ohtake, any (not necessarily strict) Morita context induces an equivalence between appropriate subcategories of the module categories of the two rings in the Morita context. These are in fact categories of firm modules for non-unital subrings. We apply this result to various Morita contexts associated to a comodule Σ of an A-coring C. This allows to extend (weak and...