Perturbation theory for linear operators denseness and bases with applications
Intro -- Preface -- Introduction -- References -- Contents -- About the Author -- Symbols Description -- 1 Basic Notations and Results -- 1.1 Spaces and Operators -- 1.1.1 Vector and Normed Spaces -- 1.1.2 Operators on Quasi-Banach Spaces -- 1.1.3 Closed and Closable Operators -- 1.1.4 Adjoint Opera...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Singapore
Springer Nature
2021
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| Online Zugang: | zbMATH |
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Tag hinzufügen | Zusammenfassung: | Intro -- Preface -- Introduction -- References -- Contents -- About the Author -- Symbols Description -- 1 Basic Notations and Results -- 1.1 Spaces and Operators -- 1.1.1 Vector and Normed Spaces -- 1.1.2 Operators on Quasi-Banach Spaces -- 1.1.3 Closed and Closable Operators -- 1.1.4 Adjoint Operator -- 1.1.5 Fredholm Operators -- 1.2 Some Notions of Spectral Theory -- 1.2.1 Closed Graph Theorem -- 1.2.2 Resolvent Set and Spectrum -- 1.2.3 Bounded Operators -- 1.2.4 Numerical Range -- 1.3 Inequalities -- 1.4 Closed Operators -- 1.4.1 Closed Operator Perturbations -- 1.4.2 A-Bounded, A-Closed, and A-Closable -- 1.5 Lebesgue-Dominated Convergence Theorem -- 1.6 Compact, Weakly Compact, Strictly Singular … -- 1.6.1 Compact Operator -- 1.6.2 Weakly Compact Operator -- 1.6.3 Strictly Singular Operator -- 1.6.4 Discrete Operator -- 1.6.5 Ascent and Descent Operators -- 1.6.6 Riesz Operator -- 1.7 A-Compact Operators -- 1.8 Dunford-Pettis Property -- 1.9 The Jeribi Essential Spectrum -- 1.9.1 Definition -- 1.9.2 A Characterization of the Jeribi Essential Spectrum -- 1.10 Jordan Chain for an Operator and Multiplicities -- 1.11 Laurent Series Expansion of the Resolvent -- 1.12 Bases -- 1.12.1 Algebraic Bases (Hamel Bases) -- 1.12.2 On a Schauder Basis -- 1.13 Normal Operator -- 1.14 Positive Operators -- 1.15 Spectrum of the Sum of Two Operators -- 1.16 Notes and Remarks -- References -- 2 Analysis with Operators -- 2.1 Projections -- 2.1.1 Generalities -- 2.1.2 Orthogonal Projection -- 2.1.3 Spectral Projection -- 2.1.4 Sum of Spectral Projection -- 2.1.5 l2-Decomposition -- 2.2 Spectral Theory of Compact and Discrete Operators -- 2.2.1 Riesz-Schauder Theorem -- 2.2.2 Discrete Operators -- 2.3 Functions -- 2.3.1 Function of Finite Order -- 2.3.2 Function of Sine Type -- 2.3.3 Generating Function in L2(0, T) -- 2.4 Phragmén-Lindelöf Theorems. |
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| Beschreibung: | xxvi, 509 Seiten Illustrationen |
| ISBN: | 9789811625275 978-981-16-2527-5 |