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.

In the group of (continuous) Jordan automorphisms, with the uniform topology, on a semisimple Banach algebra, we show that the connected component of the identity consists of automorphisms. P. Civin and B. Yood have shown that a Jordan homomorphism (that is, a homomorphism that preserves the product xoy = | (xy+yx)) from a Banach algebra onto a semisimple Banach algebra is continuous provided t...

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

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...

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 ...

It is well known that if D is a bounded derivation on a Banach algebra A and if s is an element of A satisfying [s; Ds] = 0 then Ds must be quasinilpotent. The unbounded Kleinecke-Shirokov conjecture states that the same result holds even if D is unbounded. As yet, the conjecture has neither been proved nor has a case been found where it fails. If there is a counterexample we obtain a further r...

Unless we say otherwise, every vector space we talk about is taken to be over C. A Banach algebra is a Banach space A that is also an algebra satisfying ‖AB‖ ≤ ‖A‖ ‖B‖ for A,B ∈ A. We say that A is unital if there is a nonzero element I ∈ A such that AI = A and IA = A for all A ∈ A, called a identity element. If X is a Banach space, let B(X) denote the set of bounded linear operators X → X, and...