Journal of Linear and Topological Algebra
Year:2014 | Volume:3 | Issue:4|Papers Count:6

Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we define a new product on A ÅX and generalize the module extension Banach algebras. We obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra.

The main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (briefly soft-rgb-closed set) Moreover, soft rga-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft ga-closed, soft gab-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and we investigate the relations between soft rgb-closed set and the associated soft sets. Also, the concept of soft semi-regularization of soft topology is introduced and studied their some properties. We introduce these concepts which are defined over an initial universe with a fixed set of parameters.

Let L = U3(9) be the simple projective unitary group in dimension 3 over a field with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to L. Since Aut(L)@Z4 hence almost simple groups related to L are L, L : 2 or L : 4. In fact, we prove that L, L : 2 and L : 4 are OD-characterizable.

Let j be a w*-continuous homomorphism from a dual Banach algebra to C. The notion of j-Connes amenability is studied and some characterizations is given. A type of diagonal for dual Banach algebras is defined. It is proved that the existence of such a diagonal is equivalent to j-Connes amenability. It is also shown that j-Connes amenability is equivalent to so-called j-splitting of a certain short exact sequence.

In this paper, we introduce a new concept of a y f -contractive integral type mappings and establish some new fixed point theorems in complete metric spaces.

In this article we study Steffensen method to solve nonlinear matrix equation X + ATX-1A = Q when A is a normal matrix. We establish some conditions that generate a sequence of positive definite matrices which converges to solution of this equation.