Spectral theory of bounded linear operators:
This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and...
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Birkhäuser
[2020]
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| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems are included and presented with precision and clarity, especially for the spectral theorems, allowing students to thoroughly familiarize themselves with all the important concepts.Covering both basic and more advanced material, the five chapters and two appendices of this volume provide a modern treatment on spectral theory. Topics range from spectral results on the Banach algebra of bounded linear operators acting on Banach spaces to functional calculus for Hilbert and Banach-space operators, including Fredholm and multiplicity theories. Supplementary propositions and further notes are included as well, ensuring a wide range of topics in spectral theory are covered.Spectral Theory of Bounded Linear Operators is ideal for graduate students in mathematics, and will also appeal to a wider audience of statisticians, engineers, and physicists. Though it is mostly self-contained, a familiarity with functional analysis, especially operator theory, will be helpful. |
| Beschreibung: | xii, 249 Seiten |
| ISBN: | 9783030331511 |
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| 505 | 8 | |a Preface.- Introductory Results.- Spectrum of an Operator.- The Spectral Theorem.- Functional Calculi.- Fredholm Theory in Hilbert Space.- Aspects of Fredholm Theory in Banach Space.- A Glimpse at Multiplicity Theory. | |
| 520 | 3 | |a This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems are included and presented with precision and clarity, especially for the spectral theorems, allowing students to thoroughly familiarize themselves with all the important concepts.Covering both basic and more advanced material, the five chapters and two appendices of this volume provide a modern treatment on spectral theory. Topics range from spectral results on the Banach algebra of bounded linear operators acting on Banach spaces to functional calculus for Hilbert and Banach-space operators, including Fredholm and multiplicity theories. Supplementary propositions and further notes are included as well, ensuring a wide range of topics in spectral theory are covered.Spectral Theory of Bounded Linear Operators is ideal for graduate students in mathematics, and will also appeal to a wider audience of statisticians, engineers, and physicists. Though it is mostly self-contained, a familiarity with functional analysis, especially operator theory, will be helpful. | |
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| 653 | |a Angewandte Mathematik, Mathematische Modelle | ||
| 653 | |a B | ||
| 653 | |a Operator Theory | ||
| 653 | |a Mathematics and Statistics | ||
| 653 | |a Functional Analysis | ||
| 653 | |a Lineare und multilineare Algebra, Matrizentheorie | ||
| 653 | |a Funktionalanalysis | ||
| 653 | |a Theoretische Physik, Mathematische Physik, Computerphysik | ||
| 653 | |a Hardcover, Softcover / Mathematik/Analysis | ||
| 653 | 0 | |a Operator theory | |
| 653 | 0 | |a Functional analysis | |
| 653 | 0 | |a Mathematics | |
| 653 | 0 | |a Spectral theory;Spectral theorem proof;Bounded linear operators;Operator theory;Banach spaces;Hilbert spaces;Functional calculus;Fredholm theory;Multiplicity theory;Riesz-Dunford functional calculus | |
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Datensatz im Suchindex
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| adam_text | Contents VII Preface 1 Introductory Results 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Background: Notation and Terminology ....................................... Inverse Theorems on Banach Spaces .............................................. Orthogonal Structure in Hilbert Spaces......................................... Orthogonal Projections on Inner Product Spaces ........................ The Adjoint Operator on Hilbert Space ....................................... Normal and Hyponormal Operators .............................................. Orthogonal Reducing Eigenspaces.................................................. Compact Operators and the Fredholm Alternative .................... Supplementary Propositions ........................................................... 2 Spectrum of an Operator 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Basic Spectral Properties ................................................................ A Classical Partition of the Spectrum ........................................... Spectral Mapping Theorems ........................................................... Spectral Radius and Normaloid Operators .................................. Numerical Radius and Spectraloid Operators ......................... Spectrum of a Compact Operator ................................................ Supplementary Propositions ........................................................... 3 The Spectral Theorem 3.1 3.2 3.3 3.4 3.5 3.6 Spectral Theorem for Compact Operators .................................... Diagonalizable Operators
................................................................ Spectral Measure .............................................................................. Spectral Theorem: The General Case ........................................... Fuglede Theorems and Reducing Subspaces ................................ Supplementary Propositions .......................................................... 1 1 3 5 7 9 12 16 17 21 27 27 30 35 38 41 44 47 55 55 59 63 68 79 84 xi
Contents xii 4 Functional Calculi 4.1 Rudiments of Banach and C*-Algebras......................................... 4.2 Functional Calculus for Normal Operators ................................. 4.3 Analytic Functional Calculus: Riesz Functional Calculus ......... 4.4 Riesz Idempotents and the Riesz Decomposition Theorem .... 4.5 Supplementary Propositions .......................................................... 91 91 95 102 115 126 5 Fredholm Theory in Hilbert Space 131 5.1 5.2 5.3 5.4 5.5 5.6 Fredholm and Weyl Operators — Fredholm Index ................... Essential (Fredholm) Spectrum and Spectral Picture................ Riesz Points and Weyl Spectrum ................................................. Browder Operators and Browder Spectrum ................................ Remarks on Browder and Weyl Theorems .................................. Supplementary Propositions .......................................................... 131 141 153 162 178 184 Appendices A Aspects of Fredholm Theoryin Banach Space A.l A.2 A.3 A.4 A.5 Quotient Space ............................................................................... 189 Complementation ........................................................................... 196 Range-Kernel Complementation.....................................................200 Upper-Lower and Left-Right Approaches ................................... 204 Essential Spectrum and Spectral Picture Again ....................... 209 В A Glimpse at Multiplicity Theory B.l B.2 B.3 B.4 B.5 189 219 Meanings of Multiplicity
............................................................... 219 Complete Set of Unitary Invariants............................................... 220 Multiplicity Function for Compact Operators..............................221 Multiplicity-Free Normal Operators ........................................... 224 Multiplicity Function for Normal Operators ............................. 227 References 233 List of Symbols 239 Index 243
|
| adam_txt |
Contents VII Preface 1 Introductory Results 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Background: Notation and Terminology . Inverse Theorems on Banach Spaces . Orthogonal Structure in Hilbert Spaces. Orthogonal Projections on Inner Product Spaces . The Adjoint Operator on Hilbert Space . Normal and Hyponormal Operators . Orthogonal Reducing Eigenspaces. Compact Operators and the Fredholm Alternative . Supplementary Propositions . 2 Spectrum of an Operator 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Basic Spectral Properties . A Classical Partition of the Spectrum . Spectral Mapping Theorems . Spectral Radius and Normaloid Operators . Numerical Radius and Spectraloid Operators . Spectrum of a Compact Operator . Supplementary Propositions . 3 The Spectral Theorem 3.1 3.2 3.3 3.4 3.5 3.6 Spectral Theorem for Compact Operators . Diagonalizable Operators
. Spectral Measure . Spectral Theorem: The General Case . Fuglede Theorems and Reducing Subspaces . Supplementary Propositions . 1 1 3 5 7 9 12 16 17 21 27 27 30 35 38 41 44 47 55 55 59 63 68 79 84 xi
Contents xii 4 Functional Calculi 4.1 Rudiments of Banach and C*-Algebras. 4.2 Functional Calculus for Normal Operators . 4.3 Analytic Functional Calculus: Riesz Functional Calculus . 4.4 Riesz Idempotents and the Riesz Decomposition Theorem . 4.5 Supplementary Propositions . 91 91 95 102 115 126 5 Fredholm Theory in Hilbert Space 131 5.1 5.2 5.3 5.4 5.5 5.6 Fredholm and Weyl Operators — Fredholm Index . Essential (Fredholm) Spectrum and Spectral Picture. Riesz Points and Weyl Spectrum . Browder Operators and Browder Spectrum . Remarks on Browder and Weyl Theorems . Supplementary Propositions . 131 141 153 162 178 184 Appendices A Aspects of Fredholm Theoryin Banach Space A.l A.2 A.3 A.4 A.5 Quotient Space . 189 Complementation . 196 Range-Kernel Complementation.200 Upper-Lower and Left-Right Approaches . 204 Essential Spectrum and Spectral Picture Again . 209 В A Glimpse at Multiplicity Theory B.l B.2 B.3 B.4 B.5 189 219 Meanings of Multiplicity
. 219 Complete Set of Unitary Invariants. 220 Multiplicity Function for Compact Operators.221 Multiplicity-Free Normal Operators . 224 Multiplicity Function for Normal Operators . 227 References 233 List of Symbols 239 Index 243 |
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| author | Kubrusly, Carlos S. 1947- |
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| contents | Preface.- Introductory Results.- Spectrum of an Operator.- The Spectral Theorem.- Functional Calculi.- Fredholm Theory in Hilbert Space.- Aspects of Fredholm Theory in Banach Space.- A Glimpse at Multiplicity Theory. |
| ctrlnum | (ELiSA)ELiSA-9783030331511 (OCoLC)1143007845 (DE-599)HBZHT021094732 |
| discipline | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T20:06:36Z |
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| isbn | 9783030331511 |
| language | English |
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| spelling | Kubrusly, Carlos S. 1947- Verfasser (DE-588)173093426 aut Spectral theory of bounded linear operators Carlos S. Kubrusly Cham Birkhäuser [2020] © 2020 xii, 249 Seiten txt rdacontent n rdamedia nc rdacarrier Preface.- Introductory Results.- Spectrum of an Operator.- The Spectral Theorem.- Functional Calculi.- Fredholm Theory in Hilbert Space.- Aspects of Fredholm Theory in Banach Space.- A Glimpse at Multiplicity Theory. This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems are included and presented with precision and clarity, especially for the spectral theorems, allowing students to thoroughly familiarize themselves with all the important concepts.Covering both basic and more advanced material, the five chapters and two appendices of this volume provide a modern treatment on spectral theory. Topics range from spectral results on the Banach algebra of bounded linear operators acting on Banach spaces to functional calculus for Hilbert and Banach-space operators, including Fredholm and multiplicity theories. Supplementary propositions and further notes are included as well, ensuring a wide range of topics in spectral theory are covered.Spectral Theory of Bounded Linear Operators is ideal for graduate students in mathematics, and will also appeal to a wider audience of statisticians, engineers, and physicists. Though it is mostly self-contained, a familiarity with functional analysis, especially operator theory, will be helpful. Abgeschlossener linearer Operator (DE-588)4141055-5 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Angewandte Mathematik, Mathematische Modelle B Operator Theory Mathematics and Statistics Functional Analysis Lineare und multilineare Algebra, Matrizentheorie Funktionalanalysis Theoretische Physik, Mathematische Physik, Computerphysik Hardcover, Softcover / Mathematik/Analysis Operator theory Functional analysis Mathematics Spectral theory;Spectral theorem proof;Bounded linear operators;Operator theory;Banach spaces;Hilbert spaces;Functional calculus;Fredholm theory;Multiplicity theory;Riesz-Dunford functional calculus Spektraltheorie (DE-588)4116561-5 s Abgeschlossener linearer Operator (DE-588)4141055-5 s DE-604 Erscheint auch als Online-Ausgabe doi: 10.1007/978-3-030-33149-8 978-3-030-33149-8 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033681058&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kubrusly, Carlos S. 1947- Spectral theory of bounded linear operators Preface.- Introductory Results.- Spectrum of an Operator.- The Spectral Theorem.- Functional Calculi.- Fredholm Theory in Hilbert Space.- Aspects of Fredholm Theory in Banach Space.- A Glimpse at Multiplicity Theory. Abgeschlossener linearer Operator (DE-588)4141055-5 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4141055-5 (DE-588)4116561-5 |
| title | Spectral theory of bounded linear operators |
| title_auth | Spectral theory of bounded linear operators |
| title_exact_search | Spectral theory of bounded linear operators |
| title_exact_search_txtP | Spectral theory of bounded linear operators |
| title_full | Spectral theory of bounded linear operators Carlos S. Kubrusly |
| title_fullStr | Spectral theory of bounded linear operators Carlos S. Kubrusly |
| title_full_unstemmed | Spectral theory of bounded linear operators Carlos S. Kubrusly |
| title_short | Spectral theory of bounded linear operators |
| title_sort | spectral theory of bounded linear operators |
| topic | Abgeschlossener linearer Operator (DE-588)4141055-5 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Abgeschlossener linearer Operator Spektraltheorie |
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