Theory of linear operations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
North-Holland
1987
|
| Schriftenreihe: | North-Holland mathematical library
38 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | EST: Théorie des operations linéaires <engl.> |
| Beschreibung: | X, 237 S. |
| ISBN: | 0444701842 |
Internformat
MARC
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| 100 | 1 | |a Banach, Stefan |d 1892-1945 |e Verfasser |0 (DE-588)11865697X |4 aut | |
| 240 | 1 | 0 | |a Théorie des operations linéaires |
| 245 | 1 | 0 | |a Theory of linear operations |c S. Banach |
| 264 | 1 | |a Amsterdam [u.a.] |b North-Holland |c 1987 | |
| 300 | |a X, 237 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a North-Holland mathematical library |v 38 | |
| 500 | |a EST: Théorie des operations linéaires <engl.> | ||
| 650 | 4 | |a Banach, Espaces de | |
| 650 | 7 | |a Banach, Espaces de |2 ram | |
| 650 | 4 | |a Convergence faible | |
| 650 | 4 | |a Equation Fredholm | |
| 650 | 4 | |a Equation Volterra | |
| 650 | 4 | |a Equation fonctionnelle linéaire | |
| 650 | 4 | |a Espace Banach | |
| 650 | 4 | |a Espace vectoriel normé | |
| 650 | 4 | |a Banach spaces | |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Theorie |0 (DE-588)4059787-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Linearer Operator |0 (DE-588)4167721-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804115093100691456 |
|---|---|
| adam_text | THEORY OF LINEAR OPERATIONS S. BANACH T ENGLISH TRANSLATION BY F.
JELLETT LONDON, UNITED KINGDOM 1987 NORTH-HOLLAND AMSTERDAM * NEW YORK
* OXFORD TOKYO CONTENTS PREFACE V INTRODUCTION A. THE LEBESGUE-STIELTJES
INTEGRAL §1. SOME THEOREMS IN THE THEORY OF THE LEBESGUE INTEGRAL 1 §2.
SOME INEQUALITIES FOR P TH -POWER SUMMABLE FUNCTIONS 1 §3. ASYMPTOTIC
CONVERGENCE 2 §4. MEAN CONVERGENCE 2 §5. THE STIELTJES INTEGRAL 3 §6.
LEBESGUE S THEOREM 5 B. (B)-MEASURABLE SETS AND OPERATORS IN METRIC
SPACES. §7. METRIC SPACES 5 §8. SETS IN METRIC SPACES 7 §9. MAPPINGS IN
METRIC SPACES 9 CHAPTER I. GROUPS §1. DEFINITION OF G-SPACES 13 §2.
PROPERTIES OF SUB-GROUPS 13 §3. ADDITIVE AND LINEAR OPERATORS 14 §4. A
THEOREM ON THE CONDENSATION OF SINGULARITIES 15 CHAPTER II. GENERAL
VECTOR SPACES §1. DEFINITION AND ELEMENTARY PROPERTIES OF VECTOR SPACES
17 §2. EXTENSION OF ADDITIVE HOMOGENEOUS FUNCTIONALS 17 §3.
APPLICATIONS: GENERALISATION OF THE NOTIONS OF INTEGRAL, OF MEASURE AND
OF LIMIT 19 CHAPTER III. F-SPACES §1. DEFINITIONS AND PRELIMINARIES 23
§2. HOMOGENEOUS OPERATORS 24 §3. SERIES OF ELEMENTS. INVERSION OF LINEAR
OPERATORS .... 24 §4. CONTINUOUS NON-DIFFERENTIABLE FUNCTIONS . 27 §5.
THE CONTINUITY OF SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS ... 28 §6.
SYSTEMS OF LINEAR EQUATIONS IN INFINITELY MANY UNKNOWNS 29 §7. THE SPACE
S 31 CHAPTER IV. NORMED SPACES §1. DEFINITION OF NORMED VECTOR SPACES
AND OF BANACH SPACES 33 §2. PROPERTIES OF LINEAR OPERATORS. EXTENSION OF
LINEAR FUNCTIONALS . . 33 §3. . FUNDAMENTAL SETS AND TOTAL SETS 35 §4.
THE GENERAL FORM OF BOUNDED LINEAR FUNCTIONALS IN THE SPACES C,L ,C T
1/ 1 ,M AND IN THE SUBSPACES OF M 36 VIII TABLE OF CONTENTS §5. CLOSED
AND COMPLETE SEQUENCES IN THE SPACES C, L R , CAND L R . . . . 45 §6.
APPROXIMATION OF FUNCTIONS BELONGING TO C AND L R BY LINEAR COMBINA-
TIONS OF FUNCTIONS 45 §7. THE PROBLEM OF MOMENTS 46 §8. P CONDITION FOR
THE EXISTENCE OF SOLUTIONS OF CERTAIN SYSTEMS OF EQUATIONS IN INFINITELY
MANY UNKNOWNS 47 CHAPTER V. BANACH SPACES §1. LINEAR OPERATORS IN BANACH
SPACES 49 §2. THE PRINCIPLE OF CONDENSATION OF SINGULARITIES 50 §3.
COMPACTNESS IN BANACH SPACES- 52 §4. A PROPERTY OF THE SPACES L^, C AND
T V 52 §5. BANACH SPACES OF MEASURABLE FUNCTIONS 53 §6. EXAMPLES OF
BOUNDED LINEAR OPERATORS IN SOME SPECIAL BANACH SPACES. 54 §7. SOME
THEOREMS ON SUMMATION METHODS 55 CHAPTER VI. COMPACT OPERATORS §1.
COMPACT OPERATORS 59 §2. EXAMPLES OF COMPACT OPERATORS IN SOME SPECIAL
SPACES 59 §3. ADJOINT (CONJUGATE) OPERATORS 61 §4. APPLICATIONS.
EXAMPLES OF ADJOINT OPERATORS IN SOME SPECIAL SPACES 62 CHAPTER VII.
BIORTHOGONAL SEQUENCES §1. DEFINITION AND GENERAL PROPERTIES 65 §2.
BIORTHOGONAL SEQUENCES IN SOME SPECIAL SPACES 66 §3. BASES IN BANACH
SPACES 67 §4. SOME APPLICATIONS TO THE THEORY OF ORTHOGONAL EXPANSIONS
68 CHAPTER VIII. LINEAR FUNCTIONALS §1. PRELIMINARIES 71 §2. REGULARLY
CLOSED LINEAR SPACES OF LINEAR FUNCTIONALS 72 §3. TRANSFINITELY CLOSED
SETS OF BOUNDED LINEAR FUNCTIONALS 72 §4. WEAK CONVERGENCE OF BOUNDED
LINEAR FUNCTIONALS 75 §5. WEAKLY CLOSED SETS OF BOUNDED LINEAR
FUNCTIONALS IN SEPARABLE BANACH SPACES 76 §6. CONDITIONS FOR THE WEAK
CONVERGENCE OF BOUNDED LINEAR FUNCTIONALS ON THE SPACES C, IP , C AND IP
. . . 77 §7. WEAK COMPACTNESS OF BOUNDED SETS IN CERTAIN SPACES 79 §8.
WEAKLY CONTINUOUS LINEAR FUNCTIONALS DEFINED ON THE SPACE OF BOUND- ED
LINEAR FUNCTIONALS 80 CHAPTER IX. WEAKLY CONVERGENT SEQUENCES §1.
DEFINITION. CONDITIONS FOR THE WEAK CONVERGENCE OF SEQUENCES OF ELEMENTS
81 §2. WEAK CONVERGENCE OF SEQUENCES IN THE SPACES C T IP , C AND IP . .
. . 81 §3. THE RELATIONSHIP BETWEEN WEAK AND STRONG (NORM) CONVERGENCE
IN THE SPACES IP AND IP FOR P 1 84 §4. WEAKLY COMPLETE SPACES 85 §5. A
THEOREM ON WEAK CONVERGENCE 87 CHAPTER X. LINEAR FUNCTIONAL EQUATIONS
§1. RELATIONS BETWEEN BOUNDED LINEAR OPERATORS AND THEIR ADJOINTS ... 89
§2. RIESZ THEORY OF LINEAR EQUATIONS ASSOCIATED WITH COMPACT LINEAR
OPERATORS 92 §3. REGULAR VALUES AND PROPER VALUES IN LINEAR EQUATIONS 95
TABLE OF CONTENTS §4. THEOREMS OF FREDHOLM IN THE THEORY OF COMPACT
OPERATORS 97 §5. FREDHOLM INTEGRAL EQUATIONS 98 §6. VOLTERRA INTEGRAL
EQUATIONS 98 §7. SYMMETRIC INTEGRAL EQUATIONS 99 CHAPTER XI. ISOMETRY,
EQUIVALENCE, ISOMORPHISM §1. ISOMETRY 101 §2. THE SPACES L 2 AND V 101
§3. ISOMETRIC TRANSFORMATIONS OF NORMED VECTOR SPACES 101 §4. SPACES OF
CONTINUOUS REAL-VALUED FUNCTIONS 102 §5. ROTATIONS 105 §6. ISOMORPHISM
AND EQUIVALENCE 109 §7. PRODUCTS OF BANACH SPACES 110 §8. THE SPACE C AS
THE UNIVERSAL SPACE 112 §9. DUAL SPACES 113 CHAPTER XII. LINEAR
DIMENSION §1. DEFINITIONS 117 §2. LINEAR DIMENSION OF THE SPACES C AND
IP , FOR P= 1 117 §3. LINEAR DIMENSION OF THE SPACES IP AND IP FOR P 1
119 APPENDIX. WEAK CONVERGENCE IN BANACH SPACES §1. THE WEAK DERIVED
SETS OF SETS OF BOUNDED LINEAR FUNCTIONALS .... 127 §2. WEAK CONVERGENCE
OF ELEMENTS 132 REMARKS 137 INDEX OF TERMINOLOGY 157 SOME ASPECTS OF THE
PRESENT THEORY OF BANACH SPACES INTRODUCTION 163 NOTATION AND
TERMINOLOGY 163 CHAPTER I. §1. REFLEXIVE AND WEAKLY COMPACTLY GENERATED
BANACH SPACES. RELATED COUNTER EXAMPLES 165 CHAPTER II. LOCAL PROPERTIES
OF BANACH SPACES §2. THE BANACH-MAZUR DISTANCE AND PROJECTION CONSTANTS
169 §3. LOCAL REPRESENTABILITY OF BANACH SPACES 171 §4. THE MODULI OF
CONVEXITY AND SMOOTHNESS; SUPER-REFLEXIVE BANACH SPACES. UNCONDITIONALLY
CONVERGENT SERIES 174 CHAPTER III. THE APPROXIMATION PROPERTY AND BASES
§5. THE APPROXIMATION PROPERTY 179 §6. THE BOUNDED APPROXIMATION
PROPERTY 181 §7. BASES AND THEIR RELATION TO THE APPROXIMATION PROPERTY
183 §8. UNCONDITIONAL BASES 185 X TABLE OF CONTENTS CHAPTER IV. §9.
CHARACTERIZATIONS OF HILBERT SPACES IN THE CLASS OF BANACH SPACES. 189
CHAPTER V. CLASSICAL BANACH SPACES , §10. THE ISOMETRIC THEORY OF
CLASSICAL BANACH SPACES 195 §11. THE ISOMORPHIC THEORY OF _XP SPACES 199
§12. THE ISOMORPHIC STRUCTURE OF THE SPACES IP ( X) 204 CHAPTER VI. §13.
THE TOPOLOGICAL STRUCTURE OF LINEAR METRIC SPACES 209 §14. ADDED IN
PROOF 213 BIBLIOGRAPHY 217 ADDITIONAL BIBLIOGRAPHY 233
|
| any_adam_object | 1 |
| author | Banach, Stefan 1892-1945 |
| author_GND | (DE-588)11865697X |
| author_facet | Banach, Stefan 1892-1945 |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV000645745 |
| callnumber-first | Q - Science |
| callnumber-label | QA322 |
| callnumber-raw | QA322.2 |
| callnumber-search | QA322.2 |
| callnumber-sort | QA 3322.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 600 |
| classification_tum | MAT 462f MAT 472f |
| ctrlnum | (OCoLC)15533781 (DE-599)BVBBV000645745 |
| dewey-full | 515.7/32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7/32 |
| dewey-search | 515.7/32 |
| dewey-sort | 3515.7 232 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000645745 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:17:08Z |
| institution | BVB |
| isbn | 0444701842 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000402303 |
| oclc_num | 15533781 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-739 DE-20 DE-824 DE-706 DE-11 DE-188 DE-83 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-739 DE-20 DE-824 DE-706 DE-11 DE-188 DE-83 |
| physical | X, 237 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | North-Holland |
| record_format | marc |
| series | North-Holland mathematical library |
| series2 | North-Holland mathematical library |
| spelling | Banach, Stefan 1892-1945 Verfasser (DE-588)11865697X aut Théorie des operations linéaires Theory of linear operations S. Banach Amsterdam [u.a.] North-Holland 1987 X, 237 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library 38 EST: Théorie des operations linéaires <engl.> Banach, Espaces de Banach, Espaces de ram Convergence faible Equation Fredholm Equation Volterra Equation fonctionnelle linéaire Espace Banach Espace vectoriel normé Banach spaces Banach-Raum (DE-588)4004402-6 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Linearer Operator (DE-588)4167721-3 s Banach-Raum (DE-588)4004402-6 s DE-604 Theorie (DE-588)4059787-8 s 1\p DE-604 North-Holland mathematical library 38 (DE-604)BV000005206 38 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000402303&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 |
| spellingShingle | Banach, Stefan 1892-1945 Theory of linear operations North-Holland mathematical library Banach, Espaces de Banach, Espaces de ram Convergence faible Equation Fredholm Equation Volterra Equation fonctionnelle linéaire Espace Banach Espace vectoriel normé Banach spaces Banach-Raum (DE-588)4004402-6 gnd Theorie (DE-588)4059787-8 gnd Linearer Operator (DE-588)4167721-3 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4059787-8 (DE-588)4167721-3 |
| title | Theory of linear operations |
| title_alt | Théorie des operations linéaires |
| title_auth | Theory of linear operations |
| title_exact_search | Theory of linear operations |
| title_full | Theory of linear operations S. Banach |
| title_fullStr | Theory of linear operations S. Banach |
| title_full_unstemmed | Theory of linear operations S. Banach |
| title_short | Theory of linear operations |
| title_sort | theory of linear operations |
| topic | Banach, Espaces de Banach, Espaces de ram Convergence faible Equation Fredholm Equation Volterra Equation fonctionnelle linéaire Espace Banach Espace vectoriel normé Banach spaces Banach-Raum (DE-588)4004402-6 gnd Theorie (DE-588)4059787-8 gnd Linearer Operator (DE-588)4167721-3 gnd |
| topic_facet | Banach, Espaces de Convergence faible Equation Fredholm Equation Volterra Equation fonctionnelle linéaire Espace Banach Espace vectoriel normé Banach spaces Banach-Raum Theorie Linearer Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000402303&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005206 |
| work_keys_str_mv | AT banachstefan theoriedesoperationslineaires AT banachstefan theoryoflinearoperations |