Series in Banach spaces: conditional and unconditional convergence
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1997
|
| Series: | Operator theory
94 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 149 - 153 |
| Physical Description: | VIII, 156 S. |
| ISBN: | 3764354011 0817654011 |
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Record in the Search Index
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| adam_text | SERIES IN BANACH SPACES CONDITIONAL AND UNCONDITIONAL CONVERGENCE
MIKHAIL I. KADETS VLADIMIR M. KADETS TRANSLATED FROM THE RUSSIAN BY
ANDREI LACOB BIRKHAUSER VERLAG BASEL BOSTON BERLIN CONTENTS INTRODUCTION
VII NOTATIONS 1 CHAPTER 1. BACKGROUND MATERIAL §1. NUMERICAL SERIES.
RIEMANN S THEOREM 5 §2. MAIN DEFINITIONS. ELEMENTARY PROPERTIES OF
VECTOR SERIES 7 §3. PRELIMINARY MATERIAL ON REARRANGEMENTS OF SERIES OF
ELEMENTS OF A BANACH SPACE 9 CHAPTER 2. SERIES IN A FINITE-DIMENSIONAL
SPACE §1. STEINITZ S THEOREM ON THE SUM RANGE OF A SERIES 13 §2. THE
DVORETZKY-HANANI THEOREM ON PERFECTLY DIVERGENT SERIES 21 §3.
PECHERSKII S THEOREM 23 CHAPTER 3. CONDITIONAL CONVERGENCE IN AN
INFINITE- DIMENSIONAL SPACE §1. BASIC COUNTEREXAMPLES 29 §2. A SERIES
WHOSE SUM RANGE CONSISTS OF TWO POINTS 32 §3. CHOBANYAN S THEOREM 36 §4.
THE KHINCHIN INEQUALITIES AND THE THEOREM OF M. I. KADETS ON
CONDITIONALLY CONVERGENT SERIES IN L P 39 CHAPTER 4. UNCONDITIONALLY
CONVERGENT SERIES §1. THE DVORETZKY-ROGERS THEOREM 45 §2. ORLICZ S
THEOREM ON UNCONDITIONALLY CONVERGENT SERIES IN L P SPACES 49 §3.
ABSOLUTELY SUMMING OPERATORS. GROTHENDIECK S THEOREM . 52 CHAPTER 5.
ORLICZ S THEOREM AND THE STRUCTURE OF FINITE-DIMENSIONAL SUBSPACES §1.
FINITE REPRESENTABILITY 59 §2. THE SPACE CQ, C-CONVEXITY, AND ORLICZ S
THEOREM 62 §3. SURVEY ON RESULTS ON TYPE AND COTYPE 67 CONTENTS CHAPTER
6. SOME RESULTS FROM THE GENERAL THEORY OF BANACH SPACES §1. FRECHET
DIFFERENTIABILITY OF CONVEX FUNCTIONS 71 §2. DVORETZKY S THEOREM 73 §3.
BASIC SEQUENCES 79 §4. SOME APPLICATIONS TO CONDITIONALLY CONVERGENT
SERIES .... 82 CHAPTER 7. STEINITZ S THEOREM AND B-CONVEXITY §1.
CONDITIONALLY CONVERGENT SERIES IN SPACES WITH INFRATYPE 87 §2. A
TECHNIQUE FOR TRANSFERRING EXAMPLES WITH NONLINEAR SUM RANGE TO
ARBITRARY INFINITE-DIMENSIONAL BANACH SPACES ... 93 §3. SERIES IN SPACES
THAT ARE NOT B-CONVEX 97 CHAPTER 8. REARRANGEMENTS OF SERIES IN
TOPOLOGICAL VECTOR SPACES §1. WEAK AND STRONG SUM RANGE 101 §2.
REARRANGEMENTS OF SERIES OF FUNCTIONS 106 §3. BANASZCZYK S THEOREM ON
SERIES IN METRIZABLE NUCLEAR SPACES 110 APPENDIX. THE LIMIT SET OF THE
RIEMANN INTEGRAL SUMS OF A VECTOR-VALUED FUNCTION §1. FUNCTIONS VALUED
IN A .B-CONVEX SPACE 120 §2. THE EXAMPLE OF NAKAMURA AND AMEMIYA 122 §3.
SEPARABILITY OF THE SPACE AND THE STRUCTURE OF I(/) 127 §4. CONNECTION
WITH THE WEAK TOPOLOGY 131 COMMENTS TO THE EXERCISES 141 REFERENCES 149
INDEX 155
|
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| id | DE-604.BV011218121 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:05:59Z |
| institution | BVB |
| isbn | 3764354011 0817654011 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007526151 |
| oclc_num | 263629223 |
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| owner | DE-29T DE-384 DE-91G DE-BY-TUM DE-824 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 |
| owner_facet | DE-29T DE-384 DE-91G DE-BY-TUM DE-824 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 |
| physical | VIII, 156 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Kadec, Michail I. Verfasser aut Series in Banach spaces conditional and unconditional convergence Mikhail I. Kadets ; Vladimir M. Kadets Basel [u.a.] Birkhäuser 1997 VIII, 156 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 94 Literaturverz. S. 149 - 153 Banach-Raum (DE-588)4004402-6 gnd rswk-swf Konvergente Reihe (DE-588)4304017-2 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Konvergente Reihe (DE-588)4304017-2 s DE-604 Kadec, Vladimir M. Verfasser aut Operator theory 94 (DE-604)BV000000970 94 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007526151&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kadec, Michail I. Kadec, Vladimir M. Series in Banach spaces conditional and unconditional convergence Operator theory Banach-Raum (DE-588)4004402-6 gnd Konvergente Reihe (DE-588)4304017-2 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4304017-2 |
| title | Series in Banach spaces conditional and unconditional convergence |
| title_auth | Series in Banach spaces conditional and unconditional convergence |
| title_exact_search | Series in Banach spaces conditional and unconditional convergence |
| title_full | Series in Banach spaces conditional and unconditional convergence Mikhail I. Kadets ; Vladimir M. Kadets |
| title_fullStr | Series in Banach spaces conditional and unconditional convergence Mikhail I. Kadets ; Vladimir M. Kadets |
| title_full_unstemmed | Series in Banach spaces conditional and unconditional convergence Mikhail I. Kadets ; Vladimir M. Kadets |
| title_short | Series in Banach spaces |
| title_sort | series in banach spaces conditional and unconditional convergence |
| title_sub | conditional and unconditional convergence |
| topic | Banach-Raum (DE-588)4004402-6 gnd Konvergente Reihe (DE-588)4304017-2 gnd |
| topic_facet | Banach-Raum Konvergente Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007526151&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT kadecmichaili seriesinbanachspacesconditionalandunconditionalconvergence AT kadecvladimirm seriesinbanachspacesconditionalandunconditionalconvergence |