Holdings: Theory of linear operations

Theory of linear operations:

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Bibliographic Details
Main Author:	Banach, Stefan 1892-1945 (Author)
Format:	Book
Language:	English
Published:	Amsterdam [u.a.] North-Holland 1987
Series:	North-Holland mathematical library 38
Subjects:	Banach, Espaces de Convergence faible Equation Fredholm Equation Volterra Equation fonctionnelle linéaire Espace Banach Espace vectoriel normé Banach spaces Banach-Raum Theorie Linearer Operator
Online Access:	Inhaltsverzeichnis
Item Description:	EST: Théorie des operations linéaires <engl.>
Physical Description:	X, 237 S.
ISBN:	0444701842

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Record in the Search Index

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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
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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

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