A course in functional analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1990
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in mathematics
96 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 399 S. |
| ISBN: | 9780387972459 3540972455 |
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Datensatz im Suchindex
| _version_ | 1804122884577165312 |
|---|---|
| adam_text | JOHN B. CONWAY A COURSE IN FUNCTIONAL ANALYSIS SECOND EDITION SPRINGER
CONTENTS PREFACE VII PREFACE TO THE SECOND EDITION XI CHAPTER I HILBERT
SPACES §1. ELEMENTARY PROPERTIES AND EXAMPLES 1 §2. ORTHOGONALITY 7 §3.
THE RIESZ REPRESENTATION THEOREM 11 §4. ORTHONORMAL SETS OF VECTORS AND
BASES 14 §5. ISOMORPHIC HILBERT SPACES AND THE FOURIER TRANSFORM FOR THE
CIRCLE 19 §6. THE DIRECT SUM OF HILBERT SPACES 23 CHAPTER II OPERATORS
ON HILBERT SPACE §1. ELEMENTARY PROPERTIES AND EXAMPLES 26 §2. THE
ADJOINT OF AN OPERATOR 31 §3. PROJECTIONS AND IDEMPOTENTS; INVARIANT AND
REDUCING SUBSPACES 36 §4. COMPACT OPERATORS 41 §5.* THE DIAGONALIZATION
OF COMPACT SELF-ADJOINT OPERATORS 46 §6.* AN APPLICATION:
STURM-LIOUVILLE SYSTEMS 49 §7.* THE SPECTRAL THEOREM AND FUNCTIONAL
CALCULUS FOR COMPACT NORMAL OPERATORS 54 §8.* UNITARY EQUIVALENCE FOR
COMPACT NORMAL OPERATORS 60 CHAPTER III BANACH SPACES §1. ELEMENTARY
PROPERTIES AND EXAMPLES 63 §2. LINEAR OPERATORS ON NORMED SPACES 67
CONTENTS §3. FINITE DIMENSIONAL NORMED SPACES 69 §4. QUOTIENTS AND
PRODUCTS OF NORMED SPACES 70 §5. LINEAR FUNCTIONALS 73 §6. THE
HAHN-BANACH THEOREM 77 §7.* AN APPLICATION: BANACH LIMITS 82 §8.* AN
APPLICATION: RUNGE S THEOREM 83 §9.* AN APPLICATION: ORDERED VECTOR
SPACES 86 §10. THE DUAL OF A QUOTIENT SPACE AND A SUBSPACE 88 §11.
REFLEXIVE SPACES 89 §12. THE OPEN MAPPING AND CLOSED GRAPH THEOREMS 90
§13. COMPLEMENTED SUBSPACES OF A BANACH SPACE 93 §14. THE PRINCIPLE OF
UNIFORM BOUNDEDNESS 95 CHAPTER IV LOCALLY CONVEX SPACES §1. ELEMENTARY
PROPERTIES AND EXAMPLES 99 §2. METRIZABLE AND NORMABLE LOCALLY CONVEX
SPACES 105 §3. SOME GEOMETRIC CONSEQUENCES OF THE HAHN-BANACH THEOREM
108 §4.* SOME EXAMPLES OF THE DUAL SPACE OF A LOCALLY CONVEX SPACE 114
§5.* INDUCTIVE LIMITS AND THE SPACE OF DISTRIBUTIONS 116 CHAPTER V WEAK
TOPOLOGIES §1. DUALITY 124 §2. THE DUAL OF A SUBSPACE AND A QUOTIENT
SPACE 128 §3. ALAOGLU S THEOREM 130 §4. REFLEXIVITY REVISITED 131 §5.
SEPARABILITY AND METRIZABILITY 134 §6.* AN APPLICATION: THE STONE-CECH
COMPACTIFICATION 137 §7. THE KREIN-MILMAN THEOREM 141 §8. AN
APPLICATION: THE STONE-WEIERSTRASS THEOREM 145 §9.* THE SCHAUDER FIXED
POINT THEOREM 149 §10.* THE RYLL-NARDZEWSKI FIXED POINT THEOREM 151
§11.* AN APPLICATION: HAAR MEASURE ON A COMPACT GROUP 154 §12.* THE
KREIN-SMULIAN THEOREM 159 §13.* WEAK COMPACTNESS 163 CHAPTER VI LINEAR
OPERATORS ON A BANACH SPACE §1. THE ADJOINT OF A LINEAR OPERATOR 166
§2.* THE BANACH-STONE THEOREM 171 §3. COMPACT OPERATORS 173 §4.
INVARIANT SUBSPACES 178 §5. WEAKLY COMPACT OPERATORS 183 CONTENTS XV
CHAPTER VII BANACH ALGEBRAS AND SPECTRAL THEORY FOR OPERATORS ON A
BANACH SPACE §1. ELEMENTARY PROPERTIES AND EXAMPLES 187 §2. IDEALS AND
QUOTIENTS 191 §3. THE SPECTRUM 195 §4. THE RIESZ FUNCTIONAL CALCULUS 199
§5. DEPENDENCE OF THE SPECTRUM ON THE ALGEBRA 205 §6. THE SPECTRUM OF A
LINEAR OPERATOR 208 §7. THE SPECTRAL THEORY OF A COMPACT OPERATOR 214
§8. ABELIAN BANACH ALGEBRAS 218 §9.* THE GROUP ALGEBRA OF A LOCALLY
COMPACT ABELIAN GROUP 223 CHAPTER VIII C*-ALGEBRAS §1. ELEMENTARY
PROPERTIES AND EXAMPLES 232 §2. ABELIAN C*-ALGEBRAS AND THE FUNCTIONAL
CALCULUS IN C*-ALGEBRAS 236 §3. THE POSITIVE ELEMENTS IN A C*-ALGEBRA
240 §4.* IDEALS AND QUOTIENTS OF C*- ALGEBRAS 245 §5.* REPRESENTATIONS
OF C*-ALGEBRAS AND THE GELFAND-NAIMARK-SEGAL CONSTRUCTION 248 CHAPTER IX
NORMAL OPERATORS ON HILBERT SPACE §1. SPECTRAL MEASURES AND
REPRESENTATIONS OF ABELIAN C*-ALGEBRAS 255 §2. THE SPECTRAL THEOREM 262
§3. STAR-CYCLIC NORMAL OPERATORS 268 §4. SOME APPLICATIONS OF THE
SPECTRAL THEOREM 271 §5. TOPOLOGIES ON @{JF) 274 §6. COMMUTING OPERATORS
276 §7. ABELIAN VON NEUMANN ALGEBRAS 281 §8. THE FUNCTIONAL CALCULUS FOR
NORMAL OPERATORS: THE CONCLUSION OF THE SAGA 285 §9. INVARIANT SUBSPACES
FOR NORMAL OPERATORS 290 §10. MULTIPLICITY THEORY FOR NORMAL OPERATORS:
A COMPLETE SET OF UNITARY INVARIANTS 293 CHAPTER X UNBOUNDED OPERATORS
§1. BASIC PROPERTIES AND EXAMPLES 303 §2. SYMMETRIC AND SELF-ADJOINT
OPERATORS 308 §3. THE CAYLEY TRANSFORM 316 §4. UNBOUNDED NORMAL
OPERATORS AND THE SPECTRAL THEOREM 319 §5. STONE S THEOREM 327 §6. THE
FOURIER TRANSFORM AND DIFFERENTIATION 334 §7. MOMENTS 343 XVI CONTENTS
CHAPTER XI FREDHOLM THEORY §1. THE SPECTRUM REVISITED 347 §2. FREDHOLM
OPERATORS 349 §3. THE FREDHOLM INDEX 352 §4. THE ESSENTIAL SPECTRUM 358
§5. THE COMPONENTS OF Y& 362 §6. A FINER ANALYSIS OF THE SPECTRUM 363
APPENDIX A PRELIMINARIES §1. LINEAR ALGEBRA 369 §2. TOPOLOGY 371 APENDIX
B THE DUAL OF L (/I) 375 APPENDIX C THE DUAL OF C 0 (X) 378 BIBLIOGRAPHY
384 LIST OF SYMBOLS 391 INDEX 395
|
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| author | Conway, John B. 1939- |
| author_GND | (DE-588)110699882 |
| author_facet | Conway, John B. 1939- |
| author_role | aut |
| author_sort | Conway, John B. 1939- |
| author_variant | j b c jb jbc |
| building | Verbundindex |
| bvnumber | BV008548707 |
| classification_rvk | SK 600 |
| classification_tum | MAT 460f |
| ctrlnum | (OCoLC)263159039 (DE-599)BVBBV008548707 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:20:58Z |
| institution | BVB |
| isbn | 9780387972459 3540972455 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005619266 |
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| physical | XVI, 399 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Conway, John B. 1939- Verfasser (DE-588)110699882 aut A course in functional analysis John B. Conway 2. ed. New York [u.a.] Springer 1990 XVI, 399 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 96 Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Hilbert-Raum (DE-588)4159850-7 s 1\p DE-604 Banach-Raum (DE-588)4004402-6 s 2\p DE-604 Graduate texts in mathematics 96 (DE-604)BV000000067 96 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005619266&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Conway, John B. 1939- A course in functional analysis Graduate texts in mathematics Funktionalanalysis (DE-588)4018916-8 gnd Hilbert-Raum (DE-588)4159850-7 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4159850-7 (DE-588)4004402-6 |
| title | A course in functional analysis |
| title_auth | A course in functional analysis |
| title_exact_search | A course in functional analysis |
| title_full | A course in functional analysis John B. Conway |
| title_fullStr | A course in functional analysis John B. Conway |
| title_full_unstemmed | A course in functional analysis John B. Conway |
| title_short | A course in functional analysis |
| title_sort | a course in functional analysis |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd Hilbert-Raum (DE-588)4159850-7 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Funktionalanalysis Hilbert-Raum Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005619266&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
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