Morphisms and representations of a class of Banach C*-modules, called CQ*algebras, are considered. Together with a general method for constructing CQ*-algebras, two different ways of extending the GNS-representation are presented.

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

Synaptic algebras, introduced by D. Foulis, generalize different algebraic structures used so far as mathematical models of quantum mechanics: the traditional Hilbert space approach, order unit spaces, Jordan effect MV-algebras, orthomodular lattices. We study sharp and fuzzy observables on two special classes synaptic algebras: called generalized Hermitian algebras which are Banach duals. Rela...

Introduction A C∗-algebra is often thought of as the non-commutative generalization of a C(K)-space, i.e. the space of continuous functions on some locally compact Hausdorff space, vanishing at infinity. We go one step further, for we seek to compare the Banach space properties of C∗-algebras and their naturally complemented subspaces, with those of C(K)-spaces. (For a recent survey on C(K) spa...

Given a weight function τ, we introduce new class of Banach algebras with respect to denoted by C_0b(X, τ ). We provide complete solution the isomorphism problem in this class. further characterize BSE-extension and Inoue-Doss ideal associated it. As an application our results, show equivalence four statements: (i) τ) is BSE, (ii) BED, (iii) Tauberian (iv) bounded.

In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.

We investigate the stability of generalizedderivations on Banach algebras with a bounded central approximateidentity. We show that every approximate generalized derivation inthe sense of Rassias, is an exact generalized derivation. Also thestability problem of generalized derivations on the faithful Banachalgebras is investigated.

Abstract Let A and B be two unital Banach algebras

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...