This proceedings volume collects select contributions presented at the International Conference in Operator Theory held at Hammamet, Tunisia, on April 30 May 3, 2018. Edited and refereed by well-known experts in the field, this wide-ranging collection of survey and research articles presents the state of the art in the field of operator theory, covering topics such as operator and spectral theory, fixed point theory, functional analysis etc.

Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.

The concept of multivalued linear operators—or linear relations—is the one of the most exciting and influential fields of research in modern mathematics. Applications of this theory can be found in economic theory, noncooperative games, artificial intelligence, medicine, and more. This new book focuses on the theory of linear relations, responding to the lack of resources exclusively dealing with the spectral theory of multivalued linear operators. The subject of this book is the study of linear relations over real or complex Banach spaces. The main purposes are the definitions and characterization of different kinds of spectra and extending the notions of spectra that are considered for the usual one single-valued operator bounded or not bounded. The volume introduces the theory of pseudospectra of multivalued linear operators. The main topics include demicompact linear relations, essential spectra of linear relation, pseudospectra, and essential pseudospectra of linear relations. The volume will be very useful for researchers since it represents not only a collection of a previously heterogeneous material but is also an innovation through several extensions. Beginning graduate students who wish to enter the field of spectral theory of multivalued linear operators will benefit from the material covered, and expert readers will also find sources of inspiration.

This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series -convergence operators -hypercyclic set of linear operators Analytic operators in Bela Szoekefalvi-Nagy's sense Bases of the perturbed operator T( ) Frame of the perturbed operator T( ) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory

Linear Operators and Their Essential Pseudospectra provides a comprehensive study of spectral theory of linear operators defined on Banach spaces. The central items of interest in the volume include various essential spectra, but the author also considers some of the generalizations that have been studied. In recent years, spectral theory has witnessed an explosive development. This volume presents a survey of results concerning various types of essential spectra and pseudospectra in a unified, axiomatic way and also discusses several topics that are new but which relate to the concepts and methods emanating from the book. The main topics include essential spectra, essential pseudospectra, structured essential pseudospectra, and their relative sets. This volume will be very useful for several researchers since it represents not only a collection of previously heterogeneous material but also includes discussions of innovation through several extensions. As the spectral theory of operators is an important part of functional analysis and has numerous applications in many areas of mathematics, the author suggests that some modest prerequisites from functional analysis and operator theory should be in place to be accessible to newcomers and graduate students of mathematics.

The concept of multivalued linear operators-or linear relations-is the one of the most exciting and influential fields of research in modern mathematics. Applications of this theory can be found in economic theory, noncooperative games, artificial intelligence, medicine, and more. This new book focuses on the theory of linear relations, responding to the lack of resources exclusively dealing with the spectral theory of multivalued linear operators. The subject of this book is the study of linear relations over real or complex Banach spaces. The main purposes are the definitions and characterization of different kinds of spectra and extending the notions of spectra that are considered for the usual one single-valued operator bounded or not bounded. The volume introduces the theory of pseudospectra of multivalued linear operators. The main topics include demicompact linear relations, essential spectra of linear relation, pseudospectra, and essential pseudospectra of linear relations. The volume will be very useful for researchers since it represents not only a collection of a previously heterogeneous material but is also an innovation through several extensions. Beginning graduate students who wish to enter the field of spectral theory of multivalued linear operators will benefit from the material covered, and expert readers will also find sources of inspiration.

This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.

Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.

Linear Operators and Their Essential Pseudospectra provides a comprehensive study of spectral theory of linear operators defined on Banach spaces. The central items of interest in the volume include various essential spectra, but the author also considers some of the generalizations that have been studied. In recent years, spectral theory has witnessed an explosive development. This volume presents a survey of results concerning various types of essential spectra and pseudospectra in a unified, axiomatic way and also discusses several topics that are new but which relate to the concepts and methods emanating from the book. The main topics include essential spectra, essential pseudospectra, structured essential pseudospectra, and their relative sets. This volume will be very useful for several researchers since it represents not only a collection of previously heterogeneous material but also includes discussions of innovation through several extensions. As the spectral theory of operators is an important part of functional analysis and has numerous applications in many areas of mathematics, the author suggests that some modest prerequisites from functional analysis and operator theory should be in place to be accessible to newcomers and graduate students of mathematics.

This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.

Uncover the Useful Interactions of Fixed Point Theory with Topological Structures Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several extensions of Schauder's and Krasnosel'skii's fixed point theorems to the class of weakly compact operators acting on Banach spaces and algebras, particularly on spaces satisfying the Dunford-Pettis property. They also address under which conditions a 2x2 block operator matrix with single- and multi-valued nonlinear entries will have a fixed point. In addition, the book describes applications of fixed point theory to a wide range of diverse equations, including transport equations arising in the kinetic theory of gas, stationary nonlinear biological models, two-dimensional boundary-value problems arising in growing cell populations, and functional systems of integral equations. The book focuses on fixed point results under the weak topology since these problems involve the loss of compactness of mappings and/or the missing geometric and topological structure of their underlying domain.