Operator And Matrix Theory Function Spaces And Applications

This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

The Operator Theory conferences, organized by the Department of Mathematics of INCREST and the Department of Mathematics of the University of Timi~oara, are conceived as a means to promote cooperation and exchange of information between specialists in all areas of operator theory. This book comprises carefully selected papers on theory of linear operators and related fields. Original results of new research in fast developing areas are included. Several contributed papers focus on the action of linear operators in various function spaces. Recent advances in spectral theory and related topics, operators in indefinite metric spaces, dual algebras and the invariant subspace problem, operator algebras and group representations as well as applications to mathematical physics are presented. The research contacts of the Department of :viathematics of INCREST with the National Committee for Science and Technology of Romania provided means for developing the research activity in mathematics; they represent the generous framework of these meetings too. It is our pleasure to acknowledge the financial support of UNESCO which also contributed to the success of this meeting. We are indebted to Professor Israel Gohberg for including these Proceedings in the OT Series and for valuable advice in the editing process. Birkhauser Verlag was very cooperative in publishing this volume. Camelia Minculescu, Iren Nemethi and Rodica Stoenescu dealt with the difficult task of typing the whole manuscript using a Rank Xerox 860 word processor; we thank them for this exellent job.

This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

This volume collects a selected number of papers presented at the International Workshop on Operator Theory and its Applications (IWOTA) held in July 2014 at Vrije Universiteit in Amsterdam. Main developments in the broad area of operator theory are covered, with special emphasis on applications to science and engineering. The volume also presents papers dedicated to the eightieth birthday of Damir Arov and to the sixty-fifth birthday of Leiba Rodman, both leading figures in the area of operator theory and its applications, in particular, to systems theory.

This book is devoted to norm estimates for operator-valued functions of one and two operator arguments, as well as to their applications to spectrum perturbations of operators and to linear operator equations, i.e. to equations whose solutions are linear operators. Linear operator equations arise in both mathematical theory and engineering practice. The norm estimates suggested in the book have applications to the theories of ordinary differential, difference, functional-differential and integro-differential equations, as well as to the theories of integral operators and analytic functions. This book provides new tools for specialists in matrix theory and functional analysis. A significant part of the book covers the theory of triangular representations of operators that was developed by L de Branges, M S Brodskii, I C Gohberg, M G Krein, M S Livsic and other mathematicians.

Nonnegative matrices and positive operators are widely applied in science, engineering, and technology. This book provides the basic theory and several typical modern science and engineering applications of nonnegative matrices and positive operators, including the fundamental theory, methods, numerical analysis, and applications in the Google search engine, computational molecular dynamics, and wireless communications. Unique features of this book include the combination of the theories of nonnegative matrices and positive operators as well as the emphasis on applications of nonnegative matrices in the numerical analysis of positive operators, such as Markov operators and Frobenius–Perron operators both of which play key roles in the statistical and stochastic studies of dynamical systems. It can be used as a textbook for an upper level undergraduate or beginning graduate course in advanced matrix theory and/or positive operators as well as for an advanced topics course in operator theory or ergodic theory. In addition, it serves as a good reference for researchers in mathematical sciences, physical sciences, and engineering.

This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.