An element u of a norm-unital Banach algebra A is said to be unitary if u is invertible in A and satisfies ‖u‖ = ‖u−1‖ = 1. The norm-unital Banach algebra A is called unitary if the convex hull of the set of its unitary elements is norm-dense in the closed unit ball of A . If X is a complex Hilbert space, then the algebra BL(X) of all bounded linear operators on X is unitary by the Russo–Dye th...

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 ...

Let B be a strictly real commutative real Banach algebra with the carrier space Φ B. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism ρ : A → B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then ρ(A) is contained in the radical of B. 1. Introduction and results. Ring homomorphisms are mappings between two ...

let φ be a w  -continuous homomorphism from a dual banach algebra to c. the notion of φ-connes amenability is studied and some characterizations is given. a type of diagonal for dual banach algebras is dened. it is proved that the existence of such a diagonal is equivalent to φ-connes amenability. it is also shown that φ-connes amenability is equivalent to so-called φ-splitting of a certain s...

The paper presents basic concepts of the discrete system theory from the viewpoint of Banach algebras and shows that some Banach algebras of sequences are not only suitable mathematical framework for the multidimensional discrete system theory but also open ways to new models of discrete systems and lead to hitherto unknown methods of homomorphic signal processing and deconvolution. Three Banac...

In this note, the (p, q) outer generalized inverse in Banach algebra is considered, a new representation based on the (1, 5) inverse is presented. Also, we construct an iterative method for computing the (p, q) outer generalized inverse in Banach algebra. 2000 Mathematics Subject Classification: 15A09

Let A be a Banach algebra. Then A the second dual of A is a Banach algebra with first (second) Arens product. We study the Arens products of A(= (A∗∗)∗∗). We fined some conditions on A to be a left ideal in A. We fined the biggest two sided ideal I of A, in which I is a left (right) ideal of A∗∗.

Let I be any index set. We consider the Banach algebra Ce + l(I) with the Hadamard product, and prove that its Bass and topological stable ranks are both equal to 1. We also characterize divisors, maximal ideals, closed ideals and closed principal ideals. For I = N we also characterize all prime z-ideals in this Banach algebra.