Definition 1.2. (Semigroup) A binary algebra (S;⊛) is called a semigroup if it satisfies the associativity property, i.e., (α ⊛ β)⊛ γ = α⊛ (β ⊛ γ) ∀α, β, γ ∈ S. A semigroup is called commutative if α⊛ β = β ⊛ α ∀α, β ∈ S. Definition 1.3. (Identity Element) An element 1l ∈ S is said to be a left identity of the binary algebra (S;⊛) if 1l ⊛ α = α ∀α ∈ S. Similarly, an element 1r ∈ S is said to be...

Free semigroup algebras are wot-closed algebras generated by n isometries with pairwise orthogonal ranges. They were introduced in [27] as an interesting class of operator algebras in their own right. The prototype algebra, obtained from the left regular representation of the free semigroup on n letters, was introduced by Popescu [45] in connection with multi-variable non-commutative dilation t...

Several algebraic structures have been studied by many authors to discuss the relationships among them. This article aims study two structures, namely semigroup and BA-algebra, combining them in one form, BA-semigroup investigate some of its properties. paper BA-sub-semigroup, an ideal BA-homomorphism a with their Some examples are given illustrate results.

In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...

We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra An. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to a ∗-extendible representation σ. A ∗-extendible representation of An is regular if the absolutely continuous part coincides with the type L part. All known exa...

The Newtonian divided-di¤erence operators generate the nil-Coxeter algebra and semigroup. A bijective correspondence between the nil-Coxeter semigroup and the symmetric group is used to provide braid-like diagrams for the former, and corresponding Reidemeister-type moves for the relations. Conditions are given for similar relations to hold in a skew group ring. Interesting extensions of the nil...

We classify actions of finite groups on some class of C*-algebras with the Rokhlin property in terms of the Cuntz semigroup. An obstruction is obtained for the Cuntz semigroup of a C*-algebra allowing such an action. We also classify certain inductive limit actions of finite groups on a class of C*-algebras containing AI-algebras. This classification is done via the equivariant Cuntz semigroup.

‎generalizing the notion of character amenability for banach‎ ‎algebras‎, ‎we study the concept of $varphi$-connes amenability of‎ ‎a dual banach algebra $mathcal{a}$ with predual $mathcal{a}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{a}$ onto $bbb c$‎ ‎that lies in $mathcal{a}_*$‎. ‎several characterizations of‎ ‎$varphi$-connes amenability are given‎. ‎we also prove that the‎ ‎follo...