"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 a previously heterogeneous material but also includes innovation through several extensions. As the spectral theory of operators is an important part of functional analysis and has numerous applications in many parts 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 with a standard background in analysis."--Provided by publisher. Read more...
Abstract: "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 a previously heterogeneous material but also includes innovation through several extensions. As the spectral theory of operators is an important part of functional analysis and has numerous applications in many parts 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 with a standard background in analysis."--Provided by publisher
Content: Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
About the Author
Preface
1: Introduction
1.1 Essential Spectra and Relative Essential Spectra
1.2 Essential Pseudospectra
1.3 Structured Essential Pseudospectra and Relative Structured Essential Pseudospectra
1.4 Condition Pseudospectrum
1.5 Outline of Contents
2: Fundamentals
2.1 Operators
2.1.1 Linear Operators
2.1.2 Bounded Operators
2.1.3 Closed and Closable Operators
2.1.4 Adjoint Operator
2.1.5 Direct Sum
2.1.6 Resolvent Set and Spectrum
2.1.7 Compact Operators. 2.1.8 A-Defined, A-Bounded, and A-Compact Operators2.1.9 Weakly Compact and A-Weakly Compact Operators
2.1.10 Dunford-Pettis Property
2.1.11 Strictly Singular Operators
2.1.12 Strictly Cosingular
2.1.13 Perturbation Function
2.1.14 Measure of Non-Strict-Singularity
2.1.15 Semigroup Theory
2.2 Fredholm and Semi-Fredholm Operators
2.2.1 Definitions
2.2.2 Basics on Bounded Fredholm Operators
2.2.3 Basics on Unbounded Fredholm Operators
2.3 Perturbation
2.3.1 Fredholm and Semi-Fredholm Perturbations
2.3.2 Semi-Fredholm Perturbations
2.3.3 Riesz Operator. 2.8 Gap Topology2.8.1 Gap Between Two Subsets
2.8.2 Gap Between Two Operators
2.8.3 Convergence in the Generalized Sense
2.9 Quasi-Inverse Operator
2.10 Limit Inferior and Superior
3: Spectra
3.1 Essential Spectra
3.1.1 Definitions
3.1.2 Characterization of Essential Spectra
3.2 The Left and Right Jeribi Essential Spectra
3.3 S-Resolvent Set, S-Spectra, and S-Essential Spectra
3.3.1 The S-Resolvent Set
3.3.2 S-Spectra
3.3.3 S-Browder's Resolvent
3.3.4 S-Essential Spectra
3.4 Invariance of the S-Essential Spectrum
3.5 Pseudospectra
3.5.1 Pseudospectrum
3.5.2 S-Pseudospectrum.
