In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.

We study a noncommutative (operator space) version of the ‘boundary’, and in particular the Shilov boundary, of a function space. The main idea is that Hilbert C∗−modules and their properties, which we studied earlier in the operator space framework, replace certain topological tools. We include some general notes on the ‘commutative case’ of some of the topics we discuss, coming in part from j...

We give sufficient conditions that allow contractible (resp., reflexive amenable) Banach algebras to be finite-dimensional and semisimple algebras. Moreover, we show that any contractible (resp., reflexive amenable) Banach algebra in which every maximal left ideal has a Banach space complement is indeed a direct sum of finitely many full matrix algebras. Finally, we characterize Hermitian ∗-alg...

Abstract In this article, a definition of b ( α n , β ) {b}_{\left({\alpha }_{n},{\beta }_{n})} -best approximations -hypermetric spaces over Banach algebras is given. Our objective to prove the concept e...

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal...

3 ABSTRACT. We extend a p-adic spectral theorem of M. M. Vishik to a certain class of p-adic Banach algebras. This class includes inductive limits of finite-dimensional p-Banach algebras of the form B(X), where X is a p-adic Banach space of the form X ≃ Ω p (J), J being a finite nonempty set. In particular, we present a p-adic spectral theorem for p-adic UHF algebras and p-adic TUHF algebras (T...

In this paper, we study approximate identity properties, some propositions from Baker, Dales, Lau in general situations and establish relationships between the topological centers of module actions factorization properties with results group algebras. We consider under which sufficient necessary conditions Banach algebra $A\widehat{\otimes}B$ is Arens regular.