1. The norm || • || in a Banach algebra A is said to be minimal [l ] if, given any other norm || •||1 in A (with respect to which A need not be complete), the condition ||a||iá||a|| for each oG^4 implies that ||a[|i = ||a||. We shall say that || •|| is absolutely minimal if, given any other norm ||-||i whatever in A, then ||a||iè||a|| for each aEA. An absolutely minimal norm is of course minima...

In this paper, using the concept of measure of noncompactness, which is a very useful and powerful tools in nonlinear functional analysis, metric fixed point theory and integral equations, we introduce a new contraction on a Banach space. For this purpose by using of a measure of noncompactness on a finite product space, we obtain some generalizations of Darbo’s fixed-point theorem. Then, with ...

We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of Lp-spaces. We use this locally finite result to construct a coarse bi-Lipschitz embedding for proper subsets of any Lp-space into any Banach space X containing the l n p ’s. Finally using an...

We investigate the reflexivity of the isometry group and the automorphism group of some important metric linear spaces and algebras. The paper consists of the following sections: 1. Preliminaries. 2. Sequence spaces. 3. Spaces of measurable functions. 4. Hardy spaces. 5. Banach algebras of holomorphic functions. 6. Fréchet algebras of holomorphic functions. 7. Spaces of continuous functions. In...

For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.

Let A be a Banach algebra. A is called ideally amenable if for every closed ideal I of A, the first cohomology group of A with coefficients in I* is trivial. We investigate the closed ideals I for which H1 (A,I* )={0}, whenever A is weakly amenable or a biflat Banach algebra. Also we give some hereditary properties of ideal amenability.

using the hyers-ulam-rassias stability method, weinvestigate isomorphisms in banach algebras and derivations onbanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}moreover, we prove the hyers-ulam-rassias stability of homomorphismsin banach algebras and of derivations on banach ...

Let A be a Banach algebra and X a Banach A-bimodule, the derivation D : A → X is semi-inner if there are ξ, μ ∈ X such that D(a) = a.ξ − μ.a, (a ∈ A). A is called semi-amenable if every derivation D : A → X∗ is semi-inner. The dual Banach algebra A is Connes semi-amenable (resp. approximately semi-amenable) if, every D ∈ Z1w _ (A,X), for each normal, dual Banach A-bimodule X, is semi -inner (re...