Principles of functional analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
AMS
2002
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate studies in mathematics
36 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV013947212 | ||
| 003 | DE-604 | ||
| 005 | 20210113 | ||
| 007 | t| | ||
| 008 | 011009s2002 xx |||| 00||| eng d | ||
| 020 | |a 9780821828953 |9 978-0-8218-2895-3 | ||
| 020 | |a 0821828959 |9 0-8218-2895-9 | ||
| 035 | |a (OCoLC)314245782 | ||
| 035 | |a (DE-599)BVBBV013947212 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-91G |a DE-703 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 082 | 0 | |a 515.7 | |
| 082 | 0 | |a 515/.7 | |
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 084 | |a MAT 460f |2 stub | ||
| 084 | |a 47-01 |2 msc | ||
| 084 | |a 46-01 |2 msc | ||
| 100 | 1 | |a Schechter, Martin |d 1930- |e Verfasser |0 (DE-588)1042649022 |4 aut | |
| 245 | 1 | 0 | |a Principles of functional analysis |c Martin Schechter |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Providence, RI |b AMS |c 2002 | |
| 300 | |a XXI, 425 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 36 | |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1147-3 |
| 830 | 0 | |a Graduate studies in mathematics |v 36 |w (DE-604)BV009739289 |9 36 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009543813&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009543813 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 MAT 460f 2002 B 5 |
|---|---|
| DE-BY-TUM_katkey | 1258746 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040020663772 |
| DE-BY-UBR_call_number | 80/SK 600 S314(2) |
| DE-BY-UBR_katkey | 3209997 |
| DE-BY-UBR_location | 80 |
| DE-BY-UBR_media_number | 069030780472 |
| _version_ | 1822747413197094912 |
| adam_text | Contents
PREFACE TO THE SECOND EDITION xv
FROM THE PREFACE TO THE FIRST EDITION xix
Chapter 1. BASIC NOTIONS 1
§1.1. A problem from differential equations 1
§1.2. An examination of the results 6
§1.3. Examples of Banach spaces 9
§1.4. Fourier series 17
§1.5. Problems 24
Chapter 2. DUALITY 29
§2.1. The Riesz representation theorem 29
§2.2. The Hahn Banach theorem 33
§2.3. Consequences of the Hahn Banach theorem 36
§2.4. Examples of dual spaces 39
§2.5. Problems 51
Chapter 3. LINEAR OPERATORS 55
§3.1. Basic properties 55
§3.2. The adjoint operator 57
§3.3. Annihilators 59
§3.4. The inverse operator 60
§3.5. Operators with closed ranges 66
§3.6. The uniform boundedness principle 71
ix
x Contents
§3.7. The open mapping theorem 71
§3.8. Problems 72
Chapter 4. THE RIESZ THEORY FOR COMPACT OPERATORS 77
§4.1. A type of integral equation 77
§4.2. Operators of finite rank 85
§4.3. Compact operators 88
§4.4. The adjoint of a compact operator 95
§4.5. Problems 98
Chapter 5. FREDHOLM OPERATORS 101
§5.1. Orientation 101
§5.2. Further properties 105
§5.3. Perturbation theory 109
§5.4. The adjoint operator 112
§5.5. A special case 114
§5.6. Semi Fredholm operators 117
§5.7. Products of operators 123
§5.8. Problems 126
Chapter 6. SPECTRAL THEORY 129
§6.1. The spectrum and resolvent sets 129
§6.2. The spectral mapping theorem 133
§6.3. Operational calculus 134
§6.4. Spectral projections 141
§6.5. Complexification 147
§6.6. The complex Hahn Banach theorem 148
§6.7. A geometric lemma 150
§6.8. Problems 151
Chapter 7. UNBOUNDED OPERATORS 155
§7.1. Unbounded Fredholm operators 155
§7.2. Further properties 161
§7.3. Operators with closed ranges 164
§7.4. Total subsets 169
§7.5. The essential spectrum 171
§7.6. Unbounded semi Fredholm operators 173
§7.7. The adjoint of a product of operators 177
Contents xi
§7.8. Problems 179
Chapter 8. REFLEXIVE BANACH SPACES 183
§8.1. Properties of reflexive spaces 183
§8.2. Saturated subspaces 185
§8.3. Separable spaces 188
§8.4. Weak convergence 190
§8.5. Examples 192
§8.6. Completing a normed vector space 196
§8.7. Problems 197
Chapter 9. BANACH ALGEBRAS 201
§9.1. Introduction 201
§9.2. An example 205
§9.3. Commutative algebras 206
§9.4. Properties of maximal ideals 209
§9.5. Partially ordered sets 211
§9.6. Riesz operators 213
§9.7. Fredholm perturbations 215
§9.8. Semi Fredholm perturbations 216
§9.9. Remarks 222
§9.10. Problems 222
Chapter 10. SEMIGROUPS 225
§10.1. A differential equation 225
§10.2. Uniqueness 228
§10.3. Unbounded operators 229
§10.4. The infinitesimal generator 235
§10.5. An approximation theorem 238
§10.6. Problems 240
Chapter 11. HILBERT SPACE 243
§11.1. When is a Banach space a Hilbert space? 243
§11.2. Normal operators 246
§11.3. Approximation by operators of finite rank 252
§11.4. Integral operators 253
§11.5. Hyponormal operators 257
§11.6. Problems 262
xii Contents
Chapter 12. BILINEAR FORMS 265
§12.1. The numerical range 265
§12.2. The associated operator 266
§12.3. Symmetric forms 268
§12.4. Closed forms 270
§12.5. Closed extensions 274
§12.6. Closable operators 278
§12.7. Some proofs 281
§12.8. Some representation theorems 284
§12.9. Dissipative operators 285
§12.10. The case of a line or a strip 290
§12.11. Selfadjoint extensions 294
§12.12. Problems 295
Chapter 13. SELFADJOINT OPERATORS 297
§13.1. Orthogonal projections 297
§13.2. Square roots of operators 299
§13.3. A decomposition of operators 304
§13.4. Spectral resolution 306
§13.5. Some consequences 311
§13.6. Unbounded selfadjoint operators 314
§13.7. Problems 322
Chapter 14. MEASURES OF OPERATORS 325
§14.1. A seminorm 325
§14.2. Perturbation classes 329
§14.3. Related measures 332
§14.4. Measures of noncompactness 339
§14.5. The quotient space 341
§14.6. Strictly singular operators 342
§14.7. Norm perturbations 345
§14.8. Perturbation functions 350
§14.9. Factored perturbation functions 354
§14.10. Problems 357
Chapter 15. EXAMPLES AND APPLICATIONS 359
§15.1. A few remarks 359
Contents xiii
§15.2. A differential operator 360
§15.3. Does A have a closed extension? 363
§15.4. The closure of A 364
§15.5. Another approach 369
§15.6. The Fourier transform 372
§15.7. Multiplication by a function 374
§15.8. More general operators 378
§15.9. B Compactness 381
§15.10. The adjoint of A 383
§15.11. An integral operator 384
§15.12. Problems 390
Appendix A. Glossary 393
Appendix B. Major Theorems 405
Bibliography 419
Index 423
|
| any_adam_object | 1 |
| author | Schechter, Martin 1930- |
| author_GND | (DE-588)1042649022 |
| author_facet | Schechter, Martin 1930- |
| author_role | aut |
| author_sort | Schechter, Martin 1930- |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | BV013947212 |
| classification_rvk | SK 600 |
| classification_tum | MAT 460f |
| ctrlnum | (OCoLC)314245782 (DE-599)BVBBV013947212 |
| dewey-full | 515.7 515/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 515/.7 |
| dewey-search | 515.7 515/.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01603nam a2200433 cb4500</leader><controlfield tag="001">BV013947212</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210113 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">011009s2002 xx |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821828953</subfield><subfield code="9">978-0-8218-2895-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821828959</subfield><subfield code="9">0-8218-2895-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)314245782</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013947212</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.7</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.7</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 460f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">47-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">46-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Schechter, Martin</subfield><subfield code="d">1930-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1042649022</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Principles of functional analysis</subfield><subfield code="c">Martin Schechter</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">AMS</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXI, 425 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate studies in mathematics</subfield><subfield code="v">36</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-1147-3</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate studies in mathematics</subfield><subfield code="v">36</subfield><subfield code="w">(DE-604)BV009739289</subfield><subfield code="9">36</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009543813&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009543813</subfield></datafield></record></collection> |
| id | DE-604.BV013947212 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T15:44:44Z |
| institution | BVB |
| isbn | 9780821828953 0821828959 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009543813 |
| oclc_num | 314245782 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-703 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-703 DE-634 DE-83 DE-11 DE-188 |
| physical | XXI, 425 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | AMS |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spellingShingle | Schechter, Martin 1930- Principles of functional analysis Graduate studies in mathematics Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 |
| title | Principles of functional analysis |
| title_auth | Principles of functional analysis |
| title_exact_search | Principles of functional analysis |
| title_full | Principles of functional analysis Martin Schechter |
| title_fullStr | Principles of functional analysis Martin Schechter |
| title_full_unstemmed | Principles of functional analysis Martin Schechter |
| title_short | Principles of functional analysis |
| title_sort | principles of functional analysis |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009543813&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT schechtermartin principlesoffunctionalanalysis |