Hilbert space :: compact operators and the trace theorem /
Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra and advanced calculus, and develops everyth...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York, NY :
Cambridge University Press,
©1993.
|
| Schriftenreihe: | London Mathematical Society student texts ;
27. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach. Advanced undergraduates and graduate students will find that this book presents a unique introduction to operators and Hilbert space. |
| Beschreibung: | 1 online resource (xii, 131 pages) |
| Bibliographie: | Includes bibliographical references (page 126) and index. |
| ISBN: | 9781139172592 113917259X 9781107088320 1107088321 |
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| 520 | |a Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach. Advanced undergraduates and graduate students will find that this book presents a unique introduction to operators and Hilbert space. | ||
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| 505 | 8 | |a APPENDIX A: COMPACT INTEGRAL OPERATORSVIII. SQUARE ROOTS; Remarks, Exercises, and Hints; IX. THE WEAK WEYL INEQUALITY; APPENDIX B: THE WEYL INEQUALITY; Remarks, Exercises and Hints; X. IDLBERT-SCHMIDT AND TRACE CLASS OPERATORS; Remarks, Exercises and Hints; XI. THE LIDSKIJ TRACE THEOREM; Final Remarks, Exercises and Hints; APPENDIX C: LOCALIZATION OF EIGENVALUES; BIBLIOGRAPHY; Books; Research Papers; Future Reading; INDEX OF NOTATION; INDEX OF TERMS | |
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| author | Retherford, J. R. |
| author_facet | Retherford, J. R. |
| author_role | |
| author_sort | Retherford, J. R. |
| author_variant | j r r jr jrr |
| building | Verbundindex |
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| contents | Cover; Series Page; Title; Copyright; Dedication; ACKNOWLEDGEMENT; CONTENTS; INTRODUCTION; 0. THE INEQUALITIES OF IT ALL; I. PRELIMINARIES; Exercise 1. Read the introduction!; Remarks, Exercises and Hints; II. ORTHOGONALITY; Remarks, Exercises and Hints; III. ISOMORPHISMS AND ISOMETRIES; Remarks, Exercises and Hints; IV. BOUNDED LINEAR OPERATORS ON HILBERT SPACE; Remarks, Exercises, and Hints; V. ELEMENTARY SPECTRAL THEORY; Remarks, Exercises, Hints; VI. SELF-ADJOINT OPERATORS; Remarks, Exercises, and Hints; VII. COMPACT OPERATORS; Remarks, Exercises and Hints APPENDIX A: COMPACT INTEGRAL OPERATORSVIII. SQUARE ROOTS; Remarks, Exercises, and Hints; IX. THE WEAK WEYL INEQUALITY; APPENDIX B: THE WEYL INEQUALITY; Remarks, Exercises and Hints; X. IDLBERT-SCHMIDT AND TRACE CLASS OPERATORS; Remarks, Exercises and Hints; XI. THE LIDSKIJ TRACE THEOREM; Final Remarks, Exercises and Hints; APPENDIX C: LOCALIZATION OF EIGENVALUES; BIBLIOGRAPHY; Books; Research Papers; Future Reading; INDEX OF NOTATION; INDEX OF TERMS |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:03Z |
| institution | BVB |
| isbn | 9781139172592 113917259X 9781107088320 1107088321 |
| language | English |
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| series | London Mathematical Society student texts ; |
| series2 | London mathematical society student texts ; |
| spelling | Retherford, J. R. Hilbert space : compact operators and the trace theorem / J.R. Retherford. Cambridge [England] ; New York, NY : Cambridge University Press, ©1993. 1 online resource (xii, 131 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London mathematical society student texts ; 27 Includes bibliographical references (page 126) and index. Print version record. Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach. Advanced undergraduates and graduate students will find that this book presents a unique introduction to operators and Hilbert space. Cover; Series Page; Title; Copyright; Dedication; ACKNOWLEDGEMENT; CONTENTS; INTRODUCTION; 0. THE INEQUALITIES OF IT ALL; I. PRELIMINARIES; Exercise 1. Read the introduction!; Remarks, Exercises and Hints; II. ORTHOGONALITY; Remarks, Exercises and Hints; III. ISOMORPHISMS AND ISOMETRIES; Remarks, Exercises and Hints; IV. BOUNDED LINEAR OPERATORS ON HILBERT SPACE; Remarks, Exercises, and Hints; V. ELEMENTARY SPECTRAL THEORY; Remarks, Exercises, Hints; VI. SELF-ADJOINT OPERATORS; Remarks, Exercises, and Hints; VII. COMPACT OPERATORS; Remarks, Exercises and Hints APPENDIX A: COMPACT INTEGRAL OPERATORSVIII. SQUARE ROOTS; Remarks, Exercises, and Hints; IX. THE WEAK WEYL INEQUALITY; APPENDIX B: THE WEYL INEQUALITY; Remarks, Exercises and Hints; X. IDLBERT-SCHMIDT AND TRACE CLASS OPERATORS; Remarks, Exercises and Hints; XI. THE LIDSKIJ TRACE THEOREM; Final Remarks, Exercises and Hints; APPENDIX C: LOCALIZATION OF EIGENVALUES; BIBLIOGRAPHY; Books; Research Papers; Future Reading; INDEX OF NOTATION; INDEX OF TERMS Hilbert space. http://id.loc.gov/authorities/subjects/sh85060803 Espace de Hilbert. MATHEMATICS Transformations. bisacsh Hilbert space fast Hilbert-Raum gnd http://d-nb.info/gnd/4159850-7 Kompakter Operator gnd http://d-nb.info/gnd/4123545-9 Hilbertruimten. gtt Hilbert, espace de. ram has work: Hilbert space (Text) https://id.oclc.org/worldcat/entity/E39PD3MpTrqd8Pcc4CFVfyxwrV https://id.oclc.org/worldcat/ontology/hasWork Print version: Retherford, J.R. Hilbert space. Cambridge [England] ; New York, NY : Cambridge University Press, ©1993 0521418844 (DLC) 93161668 (OCoLC)28388333 London Mathematical Society student texts ; 27. http://id.loc.gov/authorities/names/n84727069 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=570394 Volltext |
| spellingShingle | Retherford, J. R. Hilbert space : compact operators and the trace theorem / London Mathematical Society student texts ; Cover; Series Page; Title; Copyright; Dedication; ACKNOWLEDGEMENT; CONTENTS; INTRODUCTION; 0. THE INEQUALITIES OF IT ALL; I. PRELIMINARIES; Exercise 1. Read the introduction!; Remarks, Exercises and Hints; II. ORTHOGONALITY; Remarks, Exercises and Hints; III. ISOMORPHISMS AND ISOMETRIES; Remarks, Exercises and Hints; IV. BOUNDED LINEAR OPERATORS ON HILBERT SPACE; Remarks, Exercises, and Hints; V. ELEMENTARY SPECTRAL THEORY; Remarks, Exercises, Hints; VI. SELF-ADJOINT OPERATORS; Remarks, Exercises, and Hints; VII. COMPACT OPERATORS; Remarks, Exercises and Hints APPENDIX A: COMPACT INTEGRAL OPERATORSVIII. SQUARE ROOTS; Remarks, Exercises, and Hints; IX. THE WEAK WEYL INEQUALITY; APPENDIX B: THE WEYL INEQUALITY; Remarks, Exercises and Hints; X. IDLBERT-SCHMIDT AND TRACE CLASS OPERATORS; Remarks, Exercises and Hints; XI. THE LIDSKIJ TRACE THEOREM; Final Remarks, Exercises and Hints; APPENDIX C: LOCALIZATION OF EIGENVALUES; BIBLIOGRAPHY; Books; Research Papers; Future Reading; INDEX OF NOTATION; INDEX OF TERMS Hilbert space. http://id.loc.gov/authorities/subjects/sh85060803 Espace de Hilbert. MATHEMATICS Transformations. bisacsh Hilbert space fast Hilbert-Raum gnd http://d-nb.info/gnd/4159850-7 Kompakter Operator gnd http://d-nb.info/gnd/4123545-9 Hilbertruimten. gtt Hilbert, espace de. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85060803 http://d-nb.info/gnd/4159850-7 http://d-nb.info/gnd/4123545-9 |
| title | Hilbert space : compact operators and the trace theorem / |
| title_auth | Hilbert space : compact operators and the trace theorem / |
| title_exact_search | Hilbert space : compact operators and the trace theorem / |
| title_full | Hilbert space : compact operators and the trace theorem / J.R. Retherford. |
| title_fullStr | Hilbert space : compact operators and the trace theorem / J.R. Retherford. |
| title_full_unstemmed | Hilbert space : compact operators and the trace theorem / J.R. Retherford. |
| title_short | Hilbert space : |
| title_sort | hilbert space compact operators and the trace theorem |
| title_sub | compact operators and the trace theorem / |
| topic | Hilbert space. http://id.loc.gov/authorities/subjects/sh85060803 Espace de Hilbert. MATHEMATICS Transformations. bisacsh Hilbert space fast Hilbert-Raum gnd http://d-nb.info/gnd/4159850-7 Kompakter Operator gnd http://d-nb.info/gnd/4123545-9 Hilbertruimten. gtt Hilbert, espace de. ram |
| topic_facet | Hilbert space. Espace de Hilbert. MATHEMATICS Transformations. Hilbert space Hilbert-Raum Kompakter Operator Hilbertruimten. Hilbert, espace de. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=570394 |
| work_keys_str_mv | AT retherfordjr hilbertspacecompactoperatorsandthetracetheorem |