a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on...

in this paper, we introduce fuzzy banach algebra and study the properties of invertible elements and its relation with opensets. we obtain some interesting results.

1. R. F. Arens, A topology for spaces of transformations, Ann. of Math. vol. 47 (1946) pp. 480-495. 2. R. F. Arens ond J. L. Kelley, Characterizations of the space of continuous functions over a compact Hausdorff space, To be published in Trans. Amer. Math. Soc. 3. S. Banach, Théorie des opérations linéaires, Warsaw, 1932. 4. G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloquium Publications...

In this paper we provide upper estimates for the global projective dimensions of smooth crossed products $$\mathscr {S}(G, A; \alpha )$$ $$G = \mathbb {R}$$ and {T}$$ a self-induced Fréchet–Arens–Michael algebra A. To do this, powerful generalization methods which are used in works Ogneva Helemskii.

Let $mathcal{R}$ be a  commutative ring with identity, let $A$ and $B$ be two $mathcal{R}$-algebras and $varphi:Blongrightarrow A$ be an $mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $Atimes_varphi B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $Atimes_varphi B$ are studied. Accordingly, $Atimes_varphi B$ is considered from th...

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

In this paper, we establish some new critical fixed point theorems for the sum $AB+C$ in a Banach algebra relative to the weak topology, where $frac{I-C}{A}$ allows to be noninvertible. In addition, a special class of Banach algebras will be considered.

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...