A C-metric algebra consists of a unital C-algebra and a Leibniz Lip-norm on the C-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital -homomorphism from a C-metric algebra to another one is necessarily Lipschitz. It results that the free product of two Lipschitz unital -homomorphisms between C-metric algebras coming from -filtrations is still a Lipschitz u...

Let A be a unital separable C∗-algebra and B = C ⊗ K, where C is a unital C∗-algebra. Let τ : A → M(B)/B be a weakly unital full essential extensions of A by B. We show that there is a bijection between a quotient group of K0(B) onto the set of strong unitary equivalence classes of weakly unital full essential extensions σ such that [σ] = [τ ] in KK(A,B). Consequently, when this group is zero, ...

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.

in this paper we investigate some hereditary properties of amenability modulo an ideal of banach algebras. we show that if (e) is a bounded approximate identity modulo i of a banach algebra a and x is a neo-unital modulo i, then (e) is a bounded approximate identity for x. moreover we show that amenability modulo an ideal of a banach algebra a can be only considered by the neo-unital modulo...

Let A be a unital AH-algebra and let α ∈ Aut(A) be an automorphism. A necessary condition for A ⋊α Z being embedded into a unital simple AF-algebra is the existence of a faithful tracial state. If in addition, there is an automorphism κ with κ∗1 = −idK1(A) such that α ◦ κ and κ ◦ α are asymptotically unitarily equivalent, then A⋊α Z can be embedded into a unital simple AF-algebra. Consequently,...

Inspired by the recent work of Bekka, we study two reasonable analogues of property (T ) for not necessarily unital C∗-algebras. The stronger one of the two is called “property (T )” and the weaker one is called “property (Te)”. It is shown that all non-unital C*-algebras do not have property (T ) (neither do their unitalizations). Moreover, all non-unital σ-unital C*-algebras do not have prope...