Akishev, G.
Published in
Advances in Operator Theory

In this paper, we consider the generalized Lorentz space of periodic functions of several variables and the Nikol’skii–Besov space of functions. The article establishes a sufficient condition for a function to belong from one generalized Lorentz space to another space in terms of the difference of the partial sums of the Fourier series of a given f...

Khare, Apoorva Rajaratnam, Bala
Published in
Advances in Operator Theory

The study of very large graphs is a prominent theme in modern-day mathematics. In this paper we develop a rigorous foundation for studying the space of finite labelled graphs and their limits. These limiting objects are naturally countable graphs, and the completed graph space G(V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasys...

Peebles, Thomas Stessin, Michael
Published in
Advances in Operator Theory

We prove that if for a pair of n×n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\times n$$\end{document} matrices A and B, with A being normal, the projective joint ...

Audeh, Wasim
Published in
Advances in Operator Theory

Audeh and Kittaneh have proved the following. Let X, Y and Z be compact operators on a complex separable Hilbert space such that XZZ∗Y≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \b...

Junis, Sawlet Oshanova, Azhar
Published in
Advances in Operator Theory

Let M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {M}}$$\end{document} be a semifinite von Neumann algebra. We proved that if xzz∗y\documentclass[12pt]{min...

Izuchukwu, Chinedu Ogbuisi, Ferdinard Udochukwu Mewomo, Oluwatosin Temitope
Published in
Advances in Operator Theory

In this paper, we introduce an iterative algorithm for approximating a common solution of Split Equality Monotone Inclusion Problem (SEMIP) and Split Equality Fixed Point Problem (SEFPP) in p-uniformly convex Banach spaces which are also uniformly smooth. Under standard and mild assumptions of monotonicity and right Bregman strongly condition of th...

de Sousa, Robert Minhós, Feliz
Published in
Advances in Operator Theory

This paper addresses the existence and location results for coupled system with two fourth-order differential equations with dependence on all derivatives in nonlinearities and subject to Lidstone-type boundary conditions. To guarantee the existence and location of the solutions, we applied lower and upper solutions technique and degree theory. In ...

Bensaid, Ikram Fatima Zohra Dehimi, Souheyb Fuglede, Bent Mortad, Mohammed Hichem
Published in
Advances in Operator Theory

In this paper, we show new versions of the Fuglede theorem in an unbounded setting. A related counterexample is also presented. In the second part of the paper, we give a pair of a closed and a self-adjoint (unbounded) operator which is not intertwined by any (bounded or closed) operator except the zero operator.

El Allali, M. Ezzaki, F.
Published in
Advances in Operator Theory

Existence of the conditional expectation of Pettis integrable random sets is proved. A Representation theorem of Pettis integrable set-valued regular martingales by regular martingales selectors is provided. As applications, Levy’s theorem convergence results are studied for Pettis integrable random sets. At the end of this paper, monotone converge...

Feki, Kais
Published in
Advances in Operator Theory

This paper is concerned with linear operators on a complex Hilbert space H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {H}$$\end{document}, which are bounde...