Introduction to Hilbert space:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Chelsea Publ. Co.
1976
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 206 S. |
| ISBN: | 0828402876 |
Internformat
MARC
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| 100 | 1 | |a Berberian, Sterling K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to Hilbert space |c Sterling K. Berberian |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Chelsea Publ. Co. |c 1976 | |
| 300 | |a 206 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Hilbert, Espace de | |
| 650 | 4 | |a Hilbert space | |
| 650 | 0 | 7 | |a Hilbert-Raum |0 (DE-588)4159850-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804135896624136192 |
|---|---|
| adam_text | Contents
Chapter I. VECTOR SPACES
§ 1. Complex vector spaces 3
§ 2. First properties of vector spaces 6
§ 3. Finite sums of vectors 7
§ 4. Linear combinations of vectors 11
§ 5. Linear subspaces, linear dependence 13
§ 6. Linear independence 17
§ 7. Basis, dimension 21
§8. Coda 24
Chapter II. HUBERT SPACES
§ 1. Pre Hilbert spaces 25
§ 2. First properties of pre Hilbert spaces 27
§ 3. The norm of a vector 28
§ 4. Metric spaces 33
§ 5. Metric notions in pre Hilbert space; Hilbert spaces 39
§ 6. Orthogonal vectors, orthonormal vectors 43
§ 7. Infinite sums in Hilbert space 49
§ 8. Total sets, separable Hilbert spaces, orthonormal bases 51
§ 9. Isomorphic Hilbert spaces; classical Hilbert space 55
Chapter III. CLOSED UNEAR SUBSPACES
§ 1. Some notations from set theory 57
§ 2. Annihilators 59
§ 3. Closed linear subspaces 62
§ 4. Complete linear subspaces 65
§ 5. Convex sets, minimizing vector 67
§ 6. Orthogonal complement 70
§ 7. Mappings 73
§8. Projection 74
i*
x Contents
Chapter IV. CONTINUOUS LINEAR MAPPINGS
§ 1. Linear mappings 77
§ 2. Isomorphic vector spaces 82
§3. The vector space £CU,W) 84
§ 4. Composition of mappings 86
§5. The algebra £(V) 88
§ 6. Continuous mappings 91
§ 7. Normed spaces, Banach spaces, continuous linear
mappings 92
§ 8. The normed space £C(S,3:) 100
§ 9. The normed algebra £C(S), Banach algebras 103
§ 10. The dual space S 104
Chapter V. CONTINUOUS LINEAR FORMS IN HUBERT SPACE
§ 1. Riesz Frechet theorem 109
§2. Completion 111
§3. Bilinear mappings 116
§ 4. Bounded bilinear mappings 120
§ 5. Sesquilinear mappings 123
§ 6. Bounded sesquilinear mappings 128
§ 7. Bounded sesquilinear forms in Hilbert space 130
§8. Adjoints 131
Chapter VI. OPERATORS IN HILBERT SPACE
§ 1. Manifesto 139
§ 2. Preliminaries 140
§ 3. An example 141
§ 4. Isometric operators 143
§ 5. Unitary operators 145
§ 6. Self adjoint operators 147
§ 7. Projection operators 151
§ 8. Normal operators 154
§ 9. Invariant and reducing subspaces 156
Chapter VII. PROPER VALUES
§ 1. Proper vectors, proper values 163
§ 2. Proper subspaces 166
§ 3. Approximate proper values 168
Contents xi
Chapter VIII. COMPLETELY CONTINUOUS OPERATORS
§ 1. Completely continuous operators 172
§ 2. An example 177
§ 3. Proper values of CC operators 178
§ 4. Spectral theorem for a normal CC operator 181
Appendix 189
Index 203
|
| adam_txt |
Contents
Chapter I. VECTOR SPACES
§ 1. Complex vector spaces 3
§ 2. First properties of vector spaces 6
§ 3. Finite sums of vectors 7
§ 4. Linear combinations of vectors 11
§ 5. Linear subspaces, linear dependence 13
§ 6. Linear independence 17
§ 7. Basis, dimension 21
§8. Coda 24
Chapter II. HUBERT SPACES
§ 1. Pre Hilbert spaces 25
§ 2. First properties of pre Hilbert spaces 27
§ 3. The norm of a vector 28
§ 4. Metric spaces 33
§ 5. Metric notions in pre Hilbert space; Hilbert spaces 39
§ 6. Orthogonal vectors, orthonormal vectors 43
§ 7. Infinite sums in Hilbert space 49
§ 8. Total sets, separable Hilbert spaces, orthonormal bases 51
§ 9. Isomorphic Hilbert spaces; classical Hilbert space 55
Chapter III. CLOSED UNEAR SUBSPACES
§ 1. Some notations from set theory 57
§ 2. Annihilators 59
§ 3. Closed linear subspaces 62
§ 4. Complete linear subspaces 65
§ 5. Convex sets, minimizing vector 67
§ 6. Orthogonal complement 70
§ 7. Mappings 73
§8. Projection 74
i*
x Contents
Chapter IV. CONTINUOUS LINEAR MAPPINGS
§ 1. Linear mappings 77
§ 2. Isomorphic vector spaces 82
§3. The vector space £CU,W) 84
§ 4. Composition of mappings 86
§5. The algebra £(V) 88
§ 6. Continuous mappings 91
§ 7. Normed spaces, Banach spaces, continuous linear
mappings 92
§ 8. The normed space £C(S,3:) 100
§ 9. The normed algebra £C(S), Banach algebras 103
§ 10. The dual space S' 104
Chapter V. CONTINUOUS LINEAR FORMS IN HUBERT SPACE
§ 1. Riesz Frechet theorem 109
§2. Completion 111
§3. Bilinear mappings 116
§ 4. Bounded bilinear mappings 120
§ 5. Sesquilinear mappings 123
§ 6. Bounded sesquilinear mappings 128
§ 7. Bounded sesquilinear forms in Hilbert space 130
§8. Adjoints 131
Chapter VI. OPERATORS IN HILBERT SPACE
§ 1. Manifesto 139
§ 2. Preliminaries 140
§ 3. An example 141
§ 4. Isometric operators 143
§ 5. Unitary operators 145
§ 6. Self adjoint operators 147
§ 7. Projection operators 151
§ 8. Normal operators 154
§ 9. Invariant and reducing subspaces 156
Chapter VII. PROPER VALUES
§ 1. Proper vectors, proper values 163
§ 2. Proper subspaces 166
§ 3. Approximate proper values 168
Contents xi
Chapter VIII. COMPLETELY CONTINUOUS OPERATORS
§ 1. Completely continuous operators 172
§ 2. An example 177
§ 3. Proper values of CC operators 178
§ 4. Spectral theorem for a normal CC operator 181
Appendix 189
Index 203 |
| any_adam_object | 1 |
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| author | Berberian, Sterling K. |
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| callnumber-subject | QA - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:06:42Z |
| indexdate | 2024-07-09T20:47:47Z |
| institution | BVB |
| isbn | 0828402876 |
| language | English |
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| spelling | Berberian, Sterling K. Verfasser aut Introduction to Hilbert space Sterling K. Berberian 2. ed. New York, NY Chelsea Publ. Co. 1976 206 S. txt rdacontent n rdamedia nc rdacarrier Hilbert, Espace de Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015152714&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berberian, Sterling K. Introduction to Hilbert space Hilbert, Espace de Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd |
| subject_GND | (DE-588)4159850-7 |
| title | Introduction to Hilbert space |
| title_auth | Introduction to Hilbert space |
| title_exact_search | Introduction to Hilbert space |
| title_exact_search_txtP | Introduction to Hilbert space |
| title_full | Introduction to Hilbert space Sterling K. Berberian |
| title_fullStr | Introduction to Hilbert space Sterling K. Berberian |
| title_full_unstemmed | Introduction to Hilbert space Sterling K. Berberian |
| title_short | Introduction to Hilbert space |
| title_sort | introduction to hilbert space |
| topic | Hilbert, Espace de Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd |
| topic_facet | Hilbert, Espace de Hilbert space Hilbert-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015152714&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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