Let F be the set of all fuzzy numbers. In this study, we embed F into a nonseparable and non-reflexive unital Banach algebra A containing F by means of a norm defined on A, which enable us to consider F as a subset of A. Besides, the Banach lattice structure of the space A according to a partial order, we define on A has been touched on.

This paper is an investigation of positive elements in a Banach algebra. Under the firmness of the state space of a Banach algebra, it is shown that even powers of positive Hermitian elements are in fact positive.

In this paper, we nd the relationships between module contractibility of aBanach algebra and its ideals. We also prove that module contractibility ofa Banach algebra is equivalent to module contractibility of its module uniti-zation. Finally, we show that when a maximal group homomorphic image ofan inverse semigroup S with the set of idempotents E is nite, the moduleprojective tensor product l1...

let  and  be banach algebras, ,  and . we define an -product on  which is a strongly splitting extension of  by . we show that these products form a large class of banach algebras which contains all module extensions and triangular banach algebras. then we consider spectrum, arens regularity, amenability and weak amenability of these products.

In this paper we study the relationships among the spectra of the cosets of an element of a Banach algebra in some quotient algebras. We also characterize the spectrum of any a E M (where M is an ideal of a Banach algebra with identity and moreover has an identity) in the whole algebra in terms of the spectrum of a in M.

We study the efficient numerical solution of infinite matrix equations Au = f for a matrix A in the Jaffard algebra. These matrices appear naturally via frame discretizations in many applications such as Gabor analysis, sampling theory, and quasi-diagonalization of pseudo-differential operators in the weighted Sjöstrand class. The proposed algorithm has two main features: firstly, it converges ...

Let *3* be the algebra of polynomials in one indeterminate x over the complex field C. Suppose || • || is a norm on 9 such that the coefficient functionals c,: X a.oc' —* a, (j = 0,1,2, • • •) are all continuous with respect to || • ||, and let K CC be the set of characters on 9> which are || • ||-continuous. Then K is compact, C\K is connected, and 0 G K. Let A be the completion of 9 with resp...

Let A be a Banach algebra, not necessarily unital, and let B be a closed subalgebra of A. We establish a connection between the Banach cyclic cohomology group HC(A) of A and the Banach B-relative cyclic cohomology group HCnB(A) of A. We prove that, for a Banach algebra A with a bounded approximate identity and an amenable closed subalgebra B of A, up to topological isomorphism, HC(A) = HCnB(A) ...

We show that if T is an isometry (as metric spaces) from an open subgroup of the invertible group A of a unital Banach algebra A onto an open subgroup of the invertible group B of a unital Banach algebra B, then T is extended to a real-linear isometry up to translation between these Banach algebras. We consider multiplicativity or unti-multiplicativity of the isometry. Note that a unital linear...