Spectral Theory Of Block Multivalued Operator Matrices
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Spectral Theory of Block Multivalued Operator Matrices
This book presents a wide panorama of methods to investigate the spectral theory of bounded and unbounded block matrices of linear relations. It explains some conditions to prove some Frobenius–Schur decompositions for linear relations and characterizes the stability of the essential spectra of these linear relations. It focuses on the study of the Fredholm theory in both Banach and Hilbert spaces, the local spectral theory of multivalued linear operators and the block matrix of linear relations. As a pioneering literature discussing spectral theory of bounded and unbounded block matrices of linear relations, this book attempts to contribute to the scarce literature on the topic. It gathers the minimum needed background material which allows a relatively friendly access to the book. Detailed proofs of all theorems are exhibited with accuracy and clarity, allowing students to thoroughly familiarize themselves with all the basic concepts.
Spectral Theory of Multivalued Linear 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.
Spectral Theory for Linear Operators
This book focuses on spectral theory for linear operators involving bounded or unbounded demicompact linear operators acting on Banach spaces. This class played an important rule in the theory of perturbation. More precisely, it contributed in the construction of several classes of stability of essential spectra for bounded or unbounded linear operators. We should emphasize that this book is the first one dealing with the demicompactness concept and its relation with Fredholm theory for bounded and unbounded linear operators as well as block operator matrices acting on Banach spaces. Researchers, as well as graduate students in applicable analysis, will find that this book constitutes a useful survey of the fundamental principles of the subject. Nevertheless, the reader is assumed to be, at least, familiar with some related sections concerning notions like the compact, Fredholm operators, the basic tools of the weak topology, the concept of measures of weak noncompactness, etc. Otherwise, the reader is urged to consult the recommended literature in order to benefit fully from this book. Features - • First book dealing with demicompactness theory and its relation with Fredholm theory for bounded and unbounded linear operators as well as block operator matrices acting on Banach spaces. • Self-contained coverage of classical and more recent classes of perturbations involving the concept of demicompactness. • Offers a useful survey of the fundamental principles of spectral theory. • Provides applications for problem arising in physics and which are modeled by integral or partial differential equations.