Abstract. For any finite unital commutative idempotent semigroup S, a unital semilattice, we show how to compute the amenability constant of its semigroup algebra l(S), which is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. Our theory applies to certain natural subalgebras of Fourier-Stieltjes alg...

Let A be a unital amenable A∗-algebra, or a unital commutative hermitian Banach ∗-algebra. We show that if ρ : A → B(H) is a bounded homomorphism, then ρ is completely bounded and ‖ρ‖cb ≤ ‖ρ‖2. Mathematics Subject Classification: 46L07; 46k05

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.

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

‎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...

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.

For a quantale I, which is unit interval endowed with continuous triangular norm and the Barr extension β¯I of ultrafilter monad to I-Rel, characterization discrete presheaf associated given. It also proved that, when & Łucasiewicz norm, isomorphic saturated prefilter monad, product prime functional ideal submonad monad.

We know from a previous paper that the reticulation of coherent quantale A is bounded distributive lattice L ( ) whose prime spectrum homeomorphic to m -prime . This studies how can be used for transferring some properties lattices quantales and vice versa. shall illustrate this thesis by proving several results on pure w –pure elements means In particular, we investigate σ –ideals transferred ...