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EN
In this paper, we introduced the notion of generalized expansive mappings in dislocated cone metric spaces with Banach algebras. Furthermore, we prove some fixed point theorems for generalized expansive mappings in dislocated cone metric spaces with Banach algebras without the assumption of normality of cones. Moreover, we give an example to elucidate our result. Our results are significant extension and generalizations of many recent results in the literature.
2
Content available remote Derivations into annihilators of the ideals of Banach algebras
EN
In this article, following Gorgi and Yazdanpanah, we define two new concepts of the ideal amenability for a Banach algebra A. We compare these notions with Ј-weak amenability and ideal amenability, where Ј is a closed two-sided ideal in A. We also study the hereditary properties of quotient ideal amenability for Banach algebras. Some examples show that the concepts of A/Ј-weak amenability and of Ј-weak amenabilitydo not coincide for Banach algebras in general.
EN
In this paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach.
4
Content available remote Maximal ideal space of certain α-Lipschitz operator algebras
EN
In a recent paper by A. Ebadian and A.A. Shokri [1], a α-Lipschitz operator from a compact metric space X into a unital bounded commutative Banach algebra B is defined. Let (X,d) be a nonempty compact metric space, 0<α≤1 and (B, || . ||) be a unital bounded commutative Banach algebra. Let Lipα(X,B) be the algebra of all bounded continuous operators ƒ: X → B such that [formula/wzor]. In this work, we characterize the maximal ideal space of Lipα(X,B).
EN
In this paper we consider the so called composition operator being a self-mapping of the Banach algebra of the function of two variables with bounded total Φ-variation in the Schramm sense. The main result of the paper characterizes the composition operator mentioned above which has a generating function being Lipschitzian with respect to the second variable. The basic tool used in our considerations is the concept of the left-left regularization.
6
Content available remote Functions of two variables with bounded φ-variation in the sense of Riesz
EN
In this paper we introduce the concept of bounded φ- variation function, in the sense of Riesz, dened in a rectangle [wzór]. We prove that the linear space [wzór] generated by the class [wzór] of all φ-bounded variation functions is a Banach algebra. Moreover, we give necessary and sucient conditions for the Nemytskii operator acting in the space [wzór] to be globally Lipschitz.
7
EN
In this paper we deal with the spectrum of the operator of the first difference A considered as an operator from E to itself where E is one of the sets [...].We apply these results to characterize matrix transformations mapping in E [...] or N. This paper generalizes some results given in [8] and [3].
8
Content available remote Pairs of derivations on rings and Banach algebras
EN
We give a generalization of Vukman's theorem concerning a pair of derivations on rings. Then applying this purely algebraic result we obtain several range inclusion results of pair of derivations on Banach algebras.
10
Content available remote A note Gateaux differentials of hermitian elements in Banach algebras
EN
Let A be a complex unital Banach algebra with unit 1. If a is an element of A is hermitian then we show that [...] and we give a proof of an inequality due to J. Nieto.
11
Content available remote On some equations related to derivations in rings and Banach algebras
EN
The main purpose of this paper is to investigate additive mapping D : R -> R, where R is a (m + n +1)! and \m2 + n2 - m - n - 4mn\ -torsion free semiprime ring with the identity element, satisfying the relation 2D(xm+n+l) = (m+-n+1)(xmD(x)xn +-xnD(x)xm), for all is an element of R and some integers m > 1, n > 1, m2 + n2 - m - n - 4mn /=0.
12
Content available remote Banach algebra homomorphisms via orthogonal projections
EN
Let A be a unital complex Banach algebra with unit e, and p1,... ,pn a collection of orthogonal projections with sum e. The aim of this note is to investigate the close connections of properties of a is an element of A and of (piapj) ia an element of Mn(A), where Mn(A) denotes the matrix algebra of all n x n matrices with entries in A.
13
Content available remote The strict topology on topological algebras
EN
In this paper, we define strict, uniform and compact-open topologies on a topological algebra and investigate their properties. These results unify and include several results of other authors.
14
Content available remote Commutativity up to a factor in Banach algebras
EN
In this note we explore commutativity up to a factor ab = alfa ba for Hermitian or normal elements of a complex Banach algebra. Our results generalize results obtained for bounded linear operators on Hilbert spaces.
15
Content available remote Spectral properties of generalized inverses
EN
Let A denote a unital complex Banach algebra. An element a € A is said to be relatively regular if aba = a for some b 6 A. Then b will be called a generalized inverse of a. In this note we study spectral properties of generalized inverses of a.
16
Content available remote Functionals on Banach algebras with scattered spectra
EN
Let A be a complex, commutative Banach algebra and let M[A] be the structure space of A. Assume that there exists a continuous homomorphism h : L^1(G) --> A with dense range, where L^1(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space M[A] is scattered (i.e., M[A] has no nonempty perfect subset). (b) Weakly almost periodic functionals on A with compact scattered spectra are almost periodic. (c) If M[A] is scattered, then the algebra A is Arens regular if and only if A* = span M[A].
17
Content available remote Universal symbols on locally compact abelian groups
EN
Let G be a locally compact abelian group, let X be its dual, let M(G) be the convolution algebra of all regular Borel measures of bounded variation on G, and let M (X) = {my | my is an element of M (G)}. A complex-valued function q on X is called symbol, if (the restriction) q|E is an element of M(X)|E for any compact subset E is a subset of X. If A is a Banach algebra then the group of invertible elements of A is denoted by A* and the spectral radius of a is an element of A is denoted by |a| . We consider continuous representations G is an element of g --> Tg is an element of A* such that ||Tg|| = 1 for all g is an element of G. In this case put my(T) = integral of GTg[my]dg). Obviously, we obtain a representation of M (G) (this representation is denoted by the same symbol T). It can easily be checked that hull(Ker(T)) is a subset of X. It leads to the correct definition of q(T) for all symbols q. Symbol q is called universal, if ||q(T)|| = |q(T)| for all T. The aim of the paper is to give a function-theoretic description of universal symbols.
18
Content available remote On some Banach algebra of infinite matrices and applications
EN
We present in this work some new se
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