Spectral Theory Of Multivalued Linear Operators

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Spectral Theory Of Multivalued Linear Operators
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Author : Aymen Ammar
language : en
Publisher: CRC Press
Release Date : 2021-09-14
Spectral Theory Of Multivalued Linear Operators written by Aymen Ammar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-14 with Mathematics categories.
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 Of Block Multivalued Operator Matrices
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Author : Aymen Ammar
language : en
Publisher: Springer
Release Date : 2025-11-19
Spectral Theory Of Block Multivalued Operator Matrices written by Aymen Ammar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-11-19 with Mathematics categories.
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.
Multivalued Linear Operators
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Author : Ronald Cross
language : en
Publisher: CRC Press
Release Date : 1998-07-09
Multivalued Linear Operators written by Ronald Cross and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-09 with Mathematics categories.
Constructs a theoretical framework for the study of linear relations and provides underlying concepts, rules, formulae, theorems and techniques. The book compares the inversion, adjoints, completion and closure of various classes of linear operators. It highlights compact and precompact relations.
Spectral Theory For Linear Operators
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Author : Bilel Krichen
language : en
Publisher: CRC Press
Release Date : 2025-08-01
Spectral Theory For Linear Operators written by Bilel Krichen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-01 with Mathematics categories.
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.
An Introduction To Local Spectral Theory
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Author : K. B. Laursen
language : en
Publisher: Oxford University Press
Release Date : 2000
An Introduction To Local Spectral Theory written by K. B. Laursen and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory, whose pioneers include Dunford, Bishop, Foias, and others. Assuming only modest prerequisites of its readership, it gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. It is highlighted by many characterizations of decomposable operators, and of other related, important classes of operators, as well as an in-depth study of their spectral properties, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Also found is a thorough and quite elementary treatment of the modern single- operator duality theory; this theory has many applications, both to general issues of classification and to such celebrated problems as the invariant subspace problems. A long chapter - almost a book in itself - is devoted to the use of local spectral theory in the study of spectral properties of multipliers and convolution operators. Another one describes its connections to automatic continuity theory. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, and extensive references. It concludes with a list of interesting open problems, suitable for continued research.
The Functional Calculus For Sectorial Operators
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Author : Markus Haase
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-18
The Functional Calculus For Sectorial Operators written by Markus Haase and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-18 with Mathematics categories.
This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.
Operator Theory Operator Algebras And Their Interactions With Geometry And Topology
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Author : Raul E Curto
language : en
Publisher: Springer Nature
Release Date : 2020-12-12
Operator Theory Operator Algebras And Their Interactions With Geometry And Topology written by Raul E Curto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-12 with Mathematics categories.
This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.
Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras
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Author : Vladimir Müller
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras written by Vladimir Müller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
Spectral theory is an important part of functional analysis.It has numerous appli cations in many parts of mathematics and physics including matrix theory, func tion theory, complex analysis, differential and integral equations, control theory and quantum physics. In recent years, spectral theory has witnessed an explosive development. There are many types of spectra, both for one or several commuting operators, with important applications, for example the approximate point spectrum, Taylor spectrum, local spectrum, essential spectrum, etc. The present monograph is an attempt to organize the available material most of which exists only in the form of research papers scattered throughout the literature. The aim is to present a survey of results concerning various types of spectra in a unified, axiomatic way. The central unifying notion is that of a regularity, which in a Banach algebra is a subset of elements that are considered to be "nice". A regularity R in a Banach algebra A defines the corresponding spectrum aR(a) = {A E C : a - ,\ rJ. R} in the same way as the ordinary spectrum is defined by means of invertible elements, a(a) = {A E C : a - ,\ rJ. Inv(A)}. Axioms of a regularity are chosen in such a way that there are many natural interesting classes satisfying them. At the same time they are strong enough for non-trivial consequences, for example the spectral mapping theorem.
Nonlinear Spectral Theory
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Author : Jürgen Appell
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Nonlinear Spectral Theory written by Jürgen Appell and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The first chapter briefly recalls the definition and properties of the spectrum and several subspectra for bounded linear operators. Then some numerical characteristics for nonlinear operators are introduced which are useful for describing those classes of operators for which there exists a spectral theory. Since spectral values are closely related to solvability results for operator equations, various conditions for the local or global invertibility of a nonlinear operator are collected in the third chapter. The following two chapters are concerned with spectra for certain classes of continuous, Lipschitz continuous, or differentiable operators. These spectra, however, simply adapt the corresponding definitions from the linear theory which somehow restricts their applicability. Other spectra which are defined in a completely different way, but seem to have useful applications, are defined and studied in the following four chapters. The remaining three chapters are more application-oriented and deal with nonlinear eigenvalue problems, numerical ranges, and selected applications to nonlinear problems. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.
The Theory Of Fractional Powers Of Operators
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Author : C. Martinez
language : en
Publisher: Elsevier
Release Date : 2001-01-17
The Theory Of Fractional Powers Of Operators written by C. Martinez and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-17 with Mathematics categories.
This book makes available to researchers and advanced graduates a simple and direct presentation of the fundamental aspects of the theory of fractional powers of non-negative operators, which have important links with partial differential equations and harmonic analysis. For the first time ever, a book deals with this subject monographically, despite the large number of papers written on it during the second half of the century. The first chapters are concerned with the construction of a basic theory of fractional powers and study the classic questions in that respect. A new and distinct feature is that the approach adopted has allowed the extension of this theory to locally convex spaces, thereby including certain differential operators, which appear naturally in distribution spaces. The bulk of the second part of the book is dedicated to powers with pure imaginary exponents, which have been the focus of research in recent years, ever since the publication in 1987 of the now classic paper by G.Dore and A.Venni. Special care has been taken to give versions of the results with more accurate hypotheses, particularly with respect to the density of the domain or the range of the operator. The authors have made a point of making the text clear and self-contained. Accordingly, an extensive appendix contains the material on real and functional analysis used and, at the end of each chapter there are detailed historical and bibliographical notes in order to understand the development and current state of research into the questions dealt with.