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...

in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.

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 ...

In this paper, we study several problems in Banach algebras concerned with the Arens products.

A properly in nite C∗-algebra has no non-zero traces. We construct properly in nite Banach ∗-algebras with non-zero, bounded traces, and show that there are even such algebras which are fairly `close' to the class of C∗-algebras, in the sense that they can be hermitian or ∗-semisimple.

It is shown that all the approximately finite dimensional C*-algebras which are not of Type I are isomorphic as Banach spaces. This generalises the matroid case given previously by Arazy. Analogous results are obtained for various families of triangular subalgebras of AF C*-algebras. In addition the classification of various continua of Type I AF C*-algebras is discussed.