Hilbert space: compact operators and the trace theorem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge <<[u.a.]>>
Cambridge Univ. Press
1993
|
| Schriftenreihe: | London Mathematical Society student texts
27 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 131 S. |
| ISBN: | 0521418844 0521429331 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV024387429 | ||
| 003 | DE-604 | ||
| 005 | 20230717 | ||
| 007 | t | ||
| 008 | 940119s1993 |||| 00||| eng d | ||
| 020 | |a 0521418844 |9 0-521-41884-4 | ||
| 020 | |a 0521429331 |9 0-521-42933-1 | ||
| 035 | |a (OCoLC)611985669 | ||
| 035 | |a (DE-599)BVBBV024387429 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-83 |a DE-188 | ||
| 084 | |a SK 620 |0 (DE-625)143249: |2 rvk | ||
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 084 | |a 47B07 |2 msc | ||
| 100 | 1 | |a Retherford, J. R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Hilbert space: compact operators and the trace theorem |c J. R. Retherford |
| 264 | 1 | |a Cambridge <<[u.a.]>> |b Cambridge Univ. Press |c 1993 | |
| 300 | |a X, 131 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society student texts |v 27 | |
| 650 | 0 | 7 | |a Hilbert-Raum |0 (DE-588)4159850-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hilbert-Raum |0 (DE-588)4159850-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a London Mathematical Society student texts |v 27 |w (DE-604)BV000841726 |9 27 | |
| 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=018366868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018366868 | ||
Datensatz im Suchindex
| _version_ | 1804140348535996416 |
|---|---|
| adam_text | CONTENTS
Introduction xi
Chapter 0 The inequalities of it all 1
Chapter I Preliminaries 3
1.1 Definition 3
1.2 Definition 4
1.3 Definition 5
1.4 Theorem 5
1.5 Theorem 6
1.6 Example 7
Chapter II Orthogonality 11
II. 1 Definition 11
11.2 Theorem H
11.3 Corollary to Bessel s inequality 13
11.4 Corollary 16
11.5 Definition 16
11.6 Definition 16
11.7 Theorem 17
11.8 The Riesz-Fischer Theorem 17
11.9 Theorem i8
11.10 Definition 18
11.11 Zorn s Lemma 19
11.12 Theorem 19
11.13 Theorem 19
H.14 Parseval s equality 20
11.15 Summary 20
11.16 Example 21
viii
Chapter III Isomorphisms and Isometries 25
Chapter IV Bounded Linear Operators on Hilbert
Space 28
IV. 1 Lemma 29
IV.2 Theorem 29
IV. 3 Theorem 30
IV.4 Riesz Representation Theorem 31
IV.5 Definition 32
Chapter V Elementary Spectral Theory 36
V.I Definition 36
V.2 Definition 36
V.3 C. Neumann expansion 37
V.4 Theorem 37
V.5 Theorem 38
V.6 Theorem 42
V.7 Theorem 44
V.8 45
V.9 Corollary 45
V.10 Spectral Radius Theorem 45
Chapter VI Self-Adjoint Operators 49
VI. 1 Definition 49
VI.2 Theorem 49
VI.3 Corollary 49
VI.4 Theorem 49
VI.5 Theorem 50
VI.6 Theorem 50
VI.7 Theorem 51
VI.8 Definition 51
VI.9 Theorem 51
VI.10 Theorem 52
VI. 11 Theorem 52
Chapter VII Compact Operators on Hilbert Space 60
VII. 1 Definition 60
VII.2 Theorem 61
ix
VII.3 The Procedure 61
VII.4 Theorem 62
VII.5 Theorem 64
Appendix A Compact Integral Operators 69
Chapter VIII Square Roots 70
VIII.l Definition 70
VIII.2 Theorem 71
VIII.3 Theorem 71
VIII.4 Theorem 72
VIII.5 Corollary 73
VIII.6 Polar Decomposition Theorem 73
VIII.7 Theorem 74
VIII.8 The Schmidt Decomposition Theorem 75
Chapter IX The Weak Weyl Inequality 78
IX. 1 Lemma 78
IX.2 Holder s Inequality 79
IX.3 Minkowski s inequality 80
IX. 4 Lemma 81
IX.5 Theorem 81
IX.6 Theorem 83
IX. 7 Theorem 85
IX.8 Weak Weyl inequality 85
Appendix B The Weyl Inequality 87
Bl Hadamard s Inequality 87
B2 Corollary 88
B3 Weyl s Inequality 89
Chapter X Hilbert-Schmidt and Trace Class
Operators 93
X.I Definition 93
X.2 Theorem 93
X.3 Theorem 94
X.4 Definition 97
X.5 Theorem 97
X.6 Theorem 98
X
X.7 Definition 99
X.8 Definition 99
X.9 Theorem 99
X.9 Corollary 100
Chapter XI The Lidskij Trace Theorem 109
XI. 1 Theorem 109
XI.2 Theorem 110
XI.3 Theorem 111
XI.4 Theorem 112
XL 5 Lemma 113
XI.6 Lemma 114
XI.7 Theorem 115
XI.8 Theorem 116
XI.9 Theorem 116
XI.10 Main Theorem 117
XL 11 Lidskij Trace Theorem 120
Appendix C Localization of Eigenvalues 124
Cl Localization of Eigenvalues 125
Bibliography 126
Index of Notation 127
Index of Terms 130
|
| any_adam_object | 1 |
| author | Retherford, J. R. |
| author_facet | Retherford, J. R. |
| author_role | aut |
| author_sort | Retherford, J. R. |
| author_variant | j r r jr jrr |
| building | Verbundindex |
| bvnumber | BV024387429 |
| classification_rvk | SK 620 SK 600 |
| ctrlnum | (OCoLC)611985669 (DE-599)BVBBV024387429 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01429nam a2200373 cb4500</leader><controlfield tag="001">BV024387429</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230717 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">940119s1993 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521418844</subfield><subfield code="9">0-521-41884-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521429331</subfield><subfield code="9">0-521-42933-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)611985669</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV024387429</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-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 620</subfield><subfield code="0">(DE-625)143249:</subfield><subfield code="2">rvk</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">47B07</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Retherford, J. R.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Hilbert space: compact operators and the trace theorem</subfield><subfield code="c">J. R. Retherford</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge <<[u.a.]>></subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 131 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">London Mathematical Society student texts</subfield><subfield code="v">27</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hilbert-Raum</subfield><subfield code="0">(DE-588)4159850-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Hilbert-Raum</subfield><subfield code="0">(DE-588)4159850-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">London Mathematical Society student texts</subfield><subfield code="v">27</subfield><subfield code="w">(DE-604)BV000841726</subfield><subfield code="9">27</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=018366868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-018366868</subfield></datafield></record></collection> |
| id | DE-604.BV024387429 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:58:33Z |
| institution | BVB |
| isbn | 0521418844 0521429331 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018366868 |
| oclc_num | 611985669 |
| open_access_boolean | |
| owner | DE-83 DE-188 |
| owner_facet | DE-83 DE-188 |
| physical | X, 131 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society student texts |
| series2 | London Mathematical Society student texts |
| spelling | Retherford, J. R. Verfasser aut Hilbert space: compact operators and the trace theorem J. R. Retherford Cambridge <<[u.a.]>> Cambridge Univ. Press 1993 X, 131 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 27 Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s DE-604 London Mathematical Society student texts 27 (DE-604)BV000841726 27 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018366868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Retherford, J. R. Hilbert space: compact operators and the trace theorem London Mathematical Society student texts Hilbert-Raum (DE-588)4159850-7 gnd |
| subject_GND | (DE-588)4159850-7 |
| 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: compact operators and the trace theorem |
| title_sort | hilbert space compact operators and the trace theorem |
| topic | Hilbert-Raum (DE-588)4159850-7 gnd |
| topic_facet | Hilbert-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018366868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000841726 |
| work_keys_str_mv | AT retherfordjr hilbertspacecompactoperatorsandthetracetheorem |