Operators In Spaces Research Articles

HARDY-CESARO MAXIMAL OPERATOR IN LEBESGUE-BMO SPACES

In this paper defining the Lebesgue-BMO spaces. We prove the boundedness of the Hardy-Cesaro maximal operators in such spaces. Also prove necessary and sufficient condition the boundedness of the Hardy-Cesaro maximal operators in Lebesgue spaces.

Rough, Soft Approximation Spaces Based on Soft Binary Relations Over ’n’ Nonempty Finite Sets

Soft, rough set theory has evolved as an essential tool for decision making. Many researchers have done a fusion of soft set and rough set over a single universe. In recent years, rough set theory, soft set theory has been extended over two different non-empty sets and fused with fuzzy sets, intuitionistic fuzzy sets, etc. This article aims to generalize soft sets over ’n’ different non-empty sets, introduce new approximation operators and topological approximation operators in approximation space and topological space, respectively and study their properties.

On some generalized numerical radius inequalities for Hilbert space operators

On some generalized numerical radius inequalities for Hilbert space operators

Convergence of the Cimmino algorithm for common fixed point problems with a countable family of operators

In this paper we apply Cimmino algorithm for common fixed point problems with a countable family of quasi-nonexpansive operators in an arbitrary normed space and show its convergence. Our results are an extension of the recent results by T. Y. Kong , H. Pajoohesh and G. T. Herman obtained for operators which are projections on convex closed sets in a finite-dimensional Euclidean space.

Similarity and approximation of EP operators

A Hilbert space operator T is called an EP operator if its range R(T) is closed and R(T)=R(T⁎). First, we show that the class of invertible operators and the class of EP operators have the same norm closure and the same interior. Second, we show that the similarity orbit of an nonzero operator T is contained in the class of EP operators if and only if T is invertible. Finally, we describe when Toeplitz operators and weighted shifts possess the EP property. We obtain similar results for an operator property weaker than the EP property.

Protected and uniformly transcendental

We show that the two-point function of protected bi-scalar operators in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM evaluated in dimensional regularization exhibits a uniform transcendental weight up to three-loop order. We conjecture that this property holds for the whole perturbative series and leverage the explicit results to postulate a prediction for the leading, order ϵ, correction to all loop orders. We also consider the soft limit of three-point functions of such operators in momentum space and point out a simple and surprising perturbative relation to two-point functions, which we also extrapolate to all loop orders.

Approximation by multivariate Baskakov–Durrmeyer operators in Orlicz spaces

Employing some properties of multivariate Baskakov–Durrmeyer operators and utilizing modified K-functional and a decomposition technique, the authors obtain the direct theorem and weak type inverse theorem in the Orlicz spaces.

An accelerated subgradient extragradient algorithm for solving bilevel variational inequality problems involving non-Lipschitz operator

In this paper, an accelerated subgradient extragradient algorithm with a new non-monotonic step size is proposed to solve bilevel variational inequality problems involving non-Lipschitz continuous operator in Hilbert spaces. The proposed algorithm with a new non-monotonic step size has the advantage of requiring only one projection onto the feasible set during each iteration and does not require prior knowledge of the Lipschitz constant of the mapping involved. Under suitable and weaker conditions, the proposed algorithm achieves strong convergence. Some numerical tests are provided to demonstrate the efficiency and advantages of the proposed algorithm against existing related algorithms.

Characterization of Lipschitz Functions via Commutators of Multilinear Singular Integral Operators in Variable Lebesgue Spaces

Characterization of Lipschitz Functions via Commutators of Multilinear Singular Integral Operators in Variable Lebesgue Spaces

On Erdélyi–Kober Fractional Operator and Quadratic Integral Equations in Orlicz Spaces

We provide and prove some new fundamental properties of the Erdélyi–Kober (EK) fractional operator, including monotonicity, boundedness, acting, and continuity in both Lebesgue spaces (Lp) and Orlicz spaces (Lφ). We employ these properties with the concept of the measure of noncompactness (MNC) associated with the fixed-point hypothesis (FPT) in solving a quadratic integral equation of fractional order in Lp,p≥1 and Lφ. Finally, we provide a few examples to support our findings. Our suppositions can be successfully applied to various fractional problems.

The quasi-similarity and dominant conditions of Weyl spectrum in a complex Hilbert space

The study of spectrum in Hilbert spaces is a very rich in giving more structures of the spectrum and we wish to go in to depth to understand deeper on the structure of the spectrum. Apart from the well-known components of spectrum i.e. spectrum, the approximate point spectrum, the point spectrum and the set of eigenvalues of finite multiplicity: there is need for further study on the Weyl spectrum of an Operator in a complex Hilbert space. To succeed in this study, two conditions to help expose properties of the Weyl spectrum i.e. Quasi-Similarity and the dominant condition will be used.

Entangled coherent states and violations of Bell-CHSH inequalities

Three classes of entangled coherent states are employed to study the Bell-CHSH inequality. By using pseudospin operators in infinite dimensional Hilbert spaces, four dichotomic operators (A,A′,B,B′) entering the inequality are constructed. For each class of coherent states, we compute the correlator 〈ψ|AB+A′B+AB′−A′B′|ψ〉, analyzing the set of parameters that leads to a Bell-CHSH inequality violation and, particularly, to the saturation of Tsirelson's bound.

Topological structure of the space of composition operators on $$L^{\!\infty }$$ of an unbounded, locally finite metric space

Topological structure of the space of composition operators on $$L^{\!\infty }$$ of an unbounded, locally finite metric space

EIGENVALUES OF STURM-LIOUVILLE PROBLEMS WITH EIGENPARAMETER DEPENDENT BOUNDARY AND INTERFACE CONDITIONS

In this paper, a regular discontinuous Sturm-Liouville problem which contains eigenparameter in both boundary and interface conditions is investigated. Firstly, a new operator associated with the problem is constructed, and the self-adjointness of the operator in an appropriate Hilbert space is proved. Some properties of eigenvalues are discussed. Finally, the continuity of eigenvalues and eigenfunctions is investigated, and the differential expressions in the sense of ordinary or Fréchet of the eigenvalues concerning the data are given.

Erratum: A unifying approach to convergence of linear sampling type operators in Orlicz spaces

Erratum for the article [1]: G. Vinti and L. Zampogni, A unifying approach to convergence of linear sampling type operators in Orlicz spaces, Advances in Differential Equations, 16 (2011), No. 5-6, 573-600.

Attraction domain analysis for steady states of Markovian open quantum systems

This article concerns the attraction domain analysis for steady states in Markovian open quantum systems, which are mathematically described by Lindblad master equations. The central question is proposed as: given a steady state, which part of the state space of density operators does it attract and which part does it not attract? We answer this question by presenting necessary and sufficient conditions that determine, for any steady state and initial state, whether the latter belongs to the attraction domain of the former. Furthermore, it is found that the attraction domain of a steady state is the intersection between the set of density operators and an affine space which contains that steady state. Moreover, we show that steady states without uniqueness in the set of density operators have attraction domains with measure zero under some translation invariant and locally finite measures. Finally, an example regarding an open Heisenberg XXZ spin chain is presented. We pick two of the system’s steady states with different magnetization profiles and analyse their attraction domains.

Eigenvalues of one-dimensional Hamiltonian operators with an eigenparameter in the boundary condition

In this paper, one-dimensional Hamiltonian operators with spectral parameter-dependent boundary conditions are investigated. First, the eigenvalues of the problem under consideration are transformed into the eigenvalues of an operator in an appropriate Hilbert space. Then, some properties of the eigenvalues are given. Moreover, the continuity and differentiability of the eigenvalues of the problem are obtained, and the differential expressions of the eigenvalues concerning each parameter are also given. Finally, Green’s function is also involved.

Analysis of wavenumber resonances for the Rayleigh system in a half space

We present a comprehensive analysis of wavenumber resonances or leaking modes associated with the Rayleigh operator in a half space containing a heterogeneous slab, being motivated by seismology. To this end, we introduce Jost solutions on an appropriate Riemann surface, a boundary matrix and a reflection matrix in analogy to the studies of scattering resonances associated with the Schrödinger operator. We analyse their analytic properties and characterize the distribution of these wavenumber resonances. Furthermore, we show that the resonances appear as poles of the meromorphic continuation of the resolvent to the nonphysical sheets of the Riemann surface as expected.

General Upper Bounds for the Numerical Radii of Powers of Hilbert Space Operators

General Upper Bounds for the Numerical Radii of Powers of Hilbert Space Operators

Spectrum of bounded operators in Hilbert spaces

This paper sought to study the spectrum operators by emphasising on condition of commuting operators so as to expose classes of operators. Here study of various classes of bounded operators on a Hilbert space H is one of the most important topics in the preparation of the study of the Hilbert spaces. In case a abounded operator A commutes at least with its own adjoint A* it forms important classes of operators on H, eg normal, unitary, self – adjoint etc. The operators under the study are bounded operators operating in a complete space called Hilbert spaces.