Entropy, compactness and the approximation of operators:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a..
Cambridge Univ. Pr.
1990
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
98 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 277 S. |
| ISBN: | 0521330114 |
Internformat
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| 100 | 1 | |a Carl, Bernd |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Entropy, compactness and the approximation of operators |c Bernd Carl ; Irmtraud Stephani |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a.. |b Cambridge Univ. Pr. |c 1990 | |
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| 490 | 1 | |a Cambridge tracts in mathematics |v 98 | |
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Datensatz im Suchindex
| _version_ | 1804118449367023616 |
|---|---|
| adam_text | Contents
Preface ix
Introduction 1
1. Entropy quantities 6
1.1. Entropy numbers of sets 6
1.2. Entropy moduli of sets 10
1.3. Entropy numbers of operators 11
1.4. Entropy moduli of operators 22
1.5. Entropy classes 26
1.6. Operator ideals 35
2. Approximation quantities 41
2.1. Approximation numbers 41
2.2. Kolmogorov numbers 48
2.3. Gelfand numbers 54
2.4. Geometrical parameters 62
2.5. Duality relations 72
2.6. Symmetrized approximation numbers 82
2.7. Local representations of approximation quantities 85
3. Inequalities of Bernstein Jackson type 95
3.1. Inequalities of Bernstein type 96
3.2. Inequalities of Jackson type 101
3.3. Geometrical parameters 105
3.4. The Hilbert space setting 115
3.5. Powers of operators 120
4. A refined Riesz theory 129
4.1. Main aspects of classical Riesz theory 130
4.2. Eigenvalues, entropy quantities, and Weyl type inequalities 139
viii Contents
4.3. Generalizations of the classical spectral radius formula 148
4.4. The Hilbert space setting 151
5. Operators with values in C(X) 159
5.1. Why C(X) valued operators? 159
5.2. Local properties of C(X) 162
5.3. Approximation quantities of C(A ) valued operators 168
5.4. The modulus of continuity of functions 170
5.5. The modulus of continuity of C(X) valued operators 174
5.6. Approximation numbers and the modulus of continuity 178
5.7. Entropy numbers and the modulus of continuity 184
5.8. Entropy properties of connected compact metric spaces 188
5.9. Holder continuous operators 196
5.10. Application of local techniques to Holder continuous
operators 199
5.11. Integral operators 212
5.12. Holder continuous integral operators 221
5.13. Operators defined by abstract kernels 225
6. Operator theoretical methods in the local theory of Banach spaces 229
6.1. Norms of projections 230
6.2. Projection constants 239
6.3. Banach Mazur distances d(M, l ) of subspaces M £ /^ 244
6.4. Volumes of convex hulls of finite sets 245
6.5. On a theorem of Pisier 248
6.6. On absolutely 1 summing and 2 summing operators 254
6.7. Tensor product techniques and the little Grothendieck
theorem 259
References 268
List of symbols 272
Index 275
|
| any_adam_object | 1 |
| author | Carl, Bernd Stephani, Irmtraud |
| author_facet | Carl, Bernd Stephani, Irmtraud |
| author_role | aut aut |
| author_sort | Carl, Bernd |
| author_variant | b c bc i s is |
| building | Verbundindex |
| bvnumber | BV004253141 |
| classification_rvk | SK 600 SK 620 |
| classification_tum | MAT 460f MAT 470f MAT 416f |
| ctrlnum | (OCoLC)246328735 (DE-599)BVBBV004253141 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV004253141 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:10:28Z |
| institution | BVB |
| isbn | 0521330114 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002645726 |
| oclc_num | 246328735 |
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| physical | X, 277 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Carl, Bernd Verfasser aut Entropy, compactness and the approximation of operators Bernd Carl ; Irmtraud Stephani 1. publ. Cambridge u.a.. Cambridge Univ. Pr. 1990 X, 277 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 98 Entropie (DE-588)4014894-4 gnd rswk-swf Kompakter Operator (DE-588)4123545-9 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Entropie (DE-588)4014894-4 s Banach-Raum (DE-588)4004402-6 s Kompakter Operator (DE-588)4123545-9 s DE-604 Linearer Operator (DE-588)4167721-3 s Operatortheorie (DE-588)4075665-8 s Funktionalanalysis (DE-588)4018916-8 s Informationstheorie (DE-588)4026927-9 s Stephani, Irmtraud Verfasser aut Cambridge tracts in mathematics 98 (DE-604)BV000000001 98 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002645726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carl, Bernd Stephani, Irmtraud Entropy, compactness and the approximation of operators Cambridge tracts in mathematics Entropie (DE-588)4014894-4 gnd Kompakter Operator (DE-588)4123545-9 gnd Informationstheorie (DE-588)4026927-9 gnd Operatortheorie (DE-588)4075665-8 gnd Linearer Operator (DE-588)4167721-3 gnd Banach-Raum (DE-588)4004402-6 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4014894-4 (DE-588)4123545-9 (DE-588)4026927-9 (DE-588)4075665-8 (DE-588)4167721-3 (DE-588)4004402-6 (DE-588)4018916-8 |
| title | Entropy, compactness and the approximation of operators |
| title_auth | Entropy, compactness and the approximation of operators |
| title_exact_search | Entropy, compactness and the approximation of operators |
| title_full | Entropy, compactness and the approximation of operators Bernd Carl ; Irmtraud Stephani |
| title_fullStr | Entropy, compactness and the approximation of operators Bernd Carl ; Irmtraud Stephani |
| title_full_unstemmed | Entropy, compactness and the approximation of operators Bernd Carl ; Irmtraud Stephani |
| title_short | Entropy, compactness and the approximation of operators |
| title_sort | entropy compactness and the approximation of operators |
| topic | Entropie (DE-588)4014894-4 gnd Kompakter Operator (DE-588)4123545-9 gnd Informationstheorie (DE-588)4026927-9 gnd Operatortheorie (DE-588)4075665-8 gnd Linearer Operator (DE-588)4167721-3 gnd Banach-Raum (DE-588)4004402-6 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Entropie Kompakter Operator Informationstheorie Operatortheorie Linearer Operator Banach-Raum Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002645726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT carlbernd entropycompactnessandtheapproximationofoperators AT stephaniirmtraud entropycompactnessandtheapproximationofoperators |