We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way...

1. Introduction Let B be a commutative Banach algebra, and let 6 be a homomorphism from B into a Banach algebra A. In this paper we are concerned with establishing conditions on A and B which ensure that 6 is continuous. If A is semisimple, it is well known that any such homomorphism must be continuous, and therefore we shall be interested in cases where A is not semisimple. Questions of this n...

in this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric connes amenability. we determine symmetric module amenability and symmetric connes amenability of some concrete banach algebras. indeed, it is shown that $ell^1(s)$ is  a symmetric $ell^1(e)$-module amenable if and only if $s$ is amenable, where $s$ is an inverse semigroup with subsemigr...

We give a structure theorem for a ring homomorphism of a commutative regular Banach algebra into another commutative Banach algebra. In particular, it is shown that: (i) A ring homomorphism of a commutative C∗-algebra onto another commutative C∗-algebra with connected infinite Gelfand space is either linear or anti-linear. (ii) A ring automorphism of L1(R ) is either linear or anti-linear. (iii...

In this paper we define the module extension dual Banach algebras and we use this Banach algebras to finding the relationship between weak−continuous homomorphisms of dual Banach algebras and Connes-amenability. So we study the weak∗−continuous derivations on module extension dual Banach algebras.

We establish versions of the Snake Lemma from homological alge bra in the context of topological groups Banach spaces and operator algebras We apply this tool to demonstrate that if f B B is a quasi unital C map of separable C algebras so that it induces a map of Corona algebras f QB QB and if f is mono then the induced map f is also mono This paper presents a cross cultural result we use ideas...

assume that $a$‎, ‎$b$ are banach algebras and that $m:atimes brightarrow b$‎, ‎$m^prime:atimes arightarrow b$ are bounded bilinear mappings‎. ‎we study the relationships between arens regularity of $m$‎, ‎$m^prime$ and the banach algebras $a$‎, ‎$b$‎. ‎for a banach $a‎$‎-bimodule $b$‎, ‎we show that $b$ factors with respect to $a$ if and only if $b^{**}$ is unital as an $a^{**}‎$‎-module‎. ‎le...

Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we define a new product on $Aoplus X$ and generalize the module extension Banach algebras. We  obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra.

i=o hold for each choice of / and g in A and k in { 1 , . . . , q}. A point derivation of infinite order is an infinite sequence {dk} of linear functional such that (1.1) holds for all k. A point derivation is continuous if each dk is continuous, totally discontinuous if dk is discontinuous for each fcSl, and degenerate if d1 = 0. Some of the terminology given in the previous paragraph was intr...