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EN
We describe the set of the scattering data for self-adjoint Sturm-Liouville operators on the half-line with potentials belonging to [formula], where [formula] is a monotonically nondecreasing function from some family R. In particular, R includes the functions [formula]
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.
3
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
The inverse scattering problem for half-line Schrodinger operators with potentials from the Marchenko class is shown to be closely related to some Banach algebra of functions on the line. In particular, it is proved that the topological conditions in the Marchenko theorem can be replaced by the condition that the scattering function should belong to this Banach algebra.
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.
6
Content available remote Closed ideals in a new class of algebras of holomorphic functions on the disc
EN
We define a new class of Banach algebras of holomorphic functions on the unit disc D which contains the algebras studied in [GMR2] and [GW]. To a function G of the class A1(D) nowhere vanishing in D we associate a Banach algebra AnG(D) contained in the disc algebra A(D). We prove that all closed ideals of AnG(D) of at most countable hull are of the standard form.
7
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.
10
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.
EN
Some inequalities for the maximum and the minimum of the spectrum for the real part of a product of two operators in Hilbert spaces are given. Applications for one operator whose transform C(...) (introduced by the author in [9]) is accretive, are given as well.
EN
This paper is devoted to discuss some generalizations of the bounded total Φ-variation in the sense of Schramm. This concept was defined by W. Schramm for functions of one real variable. In the paper we generalize the concept in question for the case of functions of of two variables defined on certain rectangle in the plane. The main result obtained in the paper asserts that the set of all functions having bounded total Φ-variation in Schramm sense has the structure of a Banach algebra.
13
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].
14
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.
16
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.
17
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.
18
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.
19
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.
20
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.
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