Infinite matrices and the gliding hump:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1996
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007528514&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 209 S. |
| ISBN: | 9810227361 |
Internformat
MARC
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| 300 | |a XI, 209 S. | ||
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| 650 | 4 | |a Functional analysis | |
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| 650 | 4 | |a Measure theory | |
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Datensatz im Suchindex
| _version_ | 1819259249711120384 |
|---|---|
| adam_text | Contents
Preface vii
1 Introduction 1
1.1 History and Summary 1
1.2 Notation and Terminology 5
2 The Antosik Mikusinski Matrix Theorem 9
2.1 Introduction 9
2.2 The Antosik Mikusinski Matrix Theorem 10
2.3 The Nikodym Convergence Theorem 16
3 ^ Convergence and £ Boundedness 21
3.1 Introduction 21
3.2 K Convergence: 21
3.3 £ Boundedness 29
3.4 ^ Spaces 33
3.5 An Abstract Hellinger Toeplitz Theorem 35
3.6 Variants of K Convergence 37
4 The Uniform Boundedness Principle 41
4.1 Introduction 41
4.2 The Uniform Boundedness Principle 41
4.3 ^ spaces 44
4.4 Equicontinuity 44
4.5 Ptak s Generalization of the UBP 46
4.6 Mate s UBP 48
4.7 The Nikodym Boundedness Theorem 51
4.8 An Abstract Uniform Boundedness Result 54
5 The Banach Steinhaus Theorem 59
5.1 Introduction 59
5.2 The General Banach Steinhaus Theorem 59
5.3 Equicontinuity 60
5.4 The Hahn Schur Summability Theorem 63
5.5 Phillips Lemma 66
ix
x CONTENTS
6 Continuity and Hypocontinuity for Bilinear Maps 69
6.1 Introduction 69
6.2 Single Bilinear Mapping 69
6.3 Families of Bilinear Maps 73
7 Pap s Adjoint Theorem 79
7.1 Introduction 79
7.2 The Adjoint Theorem 79
7.3 Closed Graph Theorem 80
8 Vector Versions of the Hahn Schur Theorems 83
8.1 Subseries Convergent Series 83
8.2 Bounded Multiplier Convergent Series 89
8.3 Other Types of Convergence for Series 95
8.4 Phillips Lemma 96
8.5 The Antosik Interchange Theorem 98
9 An Abstract Hahn Schur Theorem 101
9.1 Introduction 101
9.2 Definitions and Examples 101
9.3 The Abstract Hahn Schur Theorem 104
9.4 Special Cases 112
9.5 Other Abstract Hahn Schur Results 117
10 The Orlicz Pettis Theorem 119
10.1 Introduction 119
10.2 Normed Linear Spaces 121
10.3 Locally Convex Spaces 122
10.4 Spaces with a Schauder Basis 125
10.5 Linear Operators 129
10.6 Abstract Orlicz Pettis Theorems 132
10.7 /^ Convergence and the Orlicz Pettis Theorem 136
11 Imbedding Co and t°° 139
11.1 Introduction 139
11.2 Imbedding cq 139
11.3 Imbedding f° 145
12 Sequence Spaces 149
12.1 Introduction 149
12.2 Weak Sequential Completeness of a Duals 150
12.3 Weak Sequential Completeness of r duals 152
12.4 Weak Sequential Completeness of /? duals 155
12.5 Banach Steinhaus Results 160
xi CONTENTS
12.6 Automatic Continuity for Matrix Mappings 167
12.7 The Transpose of a Summability Matrix 174
12.8 The Kernel Theorem for Kothe Sequence Spaces 186
Index 193
References 197
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV011221103 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:08:29Z |
| institution | BVB |
| isbn | 9810227361 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007528514 |
| oclc_num | 34676775 |
| open_access_boolean | |
| owner | DE-12 DE-703 DE-824 |
| owner_facet | DE-12 DE-703 DE-824 |
| physical | XI, 209 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | World Scientific |
| record_format | marc |
| spellingShingle | Swartz, Charles 1938- Infinite matrices and the gliding hump Functional analysis Infinite matrices Measure theory Unendliche Matrix (DE-588)4285607-3 gnd |
| subject_GND | (DE-588)4285607-3 |
| title | Infinite matrices and the gliding hump |
| title_auth | Infinite matrices and the gliding hump |
| title_exact_search | Infinite matrices and the gliding hump |
| title_full | Infinite matrices and the gliding hump C. Swartz |
| title_fullStr | Infinite matrices and the gliding hump C. Swartz |
| title_full_unstemmed | Infinite matrices and the gliding hump C. Swartz |
| title_short | Infinite matrices and the gliding hump |
| title_sort | infinite matrices and the gliding hump |
| topic | Functional analysis Infinite matrices Measure theory Unendliche Matrix (DE-588)4285607-3 gnd |
| topic_facet | Functional analysis Infinite matrices Measure theory Unendliche Matrix |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007528514&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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