Banach space techniques underpinning a theory for nearly additive mappings:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Warszawa
Polska Akad. Nauk, Inst. Matematyczny
2002
|
| Schriftenreihe: | Dissertationes mathematicae
404 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 73 S. |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Titel: Banach space techniques underpinning a theory for nearly additive mappings
Autor: Cabello Sánchez, Félix
Jahr: 2002
CONTENTS
I. Ulam s stability problem and twisted sums: two. faces of a coin..............................................5
1. Background on Ulam s problem......................................................................................................5
2. Background on twisted sums..........................................................................................................9
3. Examples of nearly additive maps................................................................................................15
4. The Kalton-Peck-Ribe maps..........................................................................................................20
II. Nearly additive mappings on controlled groups............................................................................21
1. Controlled groups and asymptotically additive maps............................................................21
2. Five definitions of nearly additive maps......................................................................................22
3. Forti s example......................................................................................................................................25
4. Four stability properties....................................................................................................................26
III. Uniform boundedness principles..........................................................................................................26
1. Decomposition of groups..................................................................................................................27
2. Proof of Theorem 3.2..........................................................................................................................28
IV. Asymptotically additive maps..............................................................................................................31
1. Amenable and weakly commutative groups and semigroups..............................................31
2. Sandwich theorems..............................................................................................................................32
3. Embedding quasi-normed groups into Banach spaces............................................................38
4. The scalar case......................................................................................................................................39
5. Vector-valued maps............................................................................................................................42
V. Nearly additive mappings and exact sequences..............................................................................45
1. Quasi-normed groups as topological groups..............................................................................46
2. Extensions of quasi-normed groups..............................................................................................48
3. Nearly additive maps and twisted quasi-norms........................................................................49
4. Singular extensions of quasi-normed groups..............................................................................50
5. The behavior of nearly additive maps on dense subgroups..................................................52
6. Ger-additive maps and exact sequences......................................................................................53
VI. Duality theory and localization techniques......................................................................................55
1. The containing Banach space of a quasi-normed group........................................................55
2. Projective and almost projective groups....................................................................................58
3. Injective spaces....................................................................................................................................60
4. Sobczyk s theorem Hyers s way......................................................................................................60
5. Localization techniques......................................................................................................................62
VII. Homology sequences, and applications..............................................................................................63
1. Three-space problems....................................................................................................................65
2. iC-spaces..................................................................................................................................................66
3. C -spaces................................................................................................................................................66
4. Johnson-Lindenstrauss spaces........................................................................................................67
5. Kalton-Pelczyhski spaces..................................................................................................................68
6. The road beyond..................................................................................................................................69
References..............................................................................................................................................................69
|
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| ctrlnum | (OCoLC)50053082 (DE-599)BVBBV014571776 |
| discipline | Mathematik |
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| id | DE-604.BV014571776 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:03:45Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009907760 |
| oclc_num | 50053082 |
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| physical | 73 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Polska Akad. Nauk, Inst. Matematyczny |
| record_format | marc |
| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Cabello Sánchez, Félix Verfasser aut Banach space techniques underpinning a theory for nearly additive mappings Félix Cabello Sánchez and Jésus M. F. Castillo Warszawa Polska Akad. Nauk, Inst. Matematyczny 2002 73 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 404 Banach spaces Mappings (Mathematics) Castillo, Jesús M. F. Verfasser aut Dissertationes mathematicae 404 (DE-604)BV000003039 404 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009907760&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cabello Sánchez, Félix Castillo, Jesús M. F. Banach space techniques underpinning a theory for nearly additive mappings Dissertationes mathematicae Banach spaces Mappings (Mathematics) |
| title | Banach space techniques underpinning a theory for nearly additive mappings |
| title_auth | Banach space techniques underpinning a theory for nearly additive mappings |
| title_exact_search | Banach space techniques underpinning a theory for nearly additive mappings |
| title_full | Banach space techniques underpinning a theory for nearly additive mappings Félix Cabello Sánchez and Jésus M. F. Castillo |
| title_fullStr | Banach space techniques underpinning a theory for nearly additive mappings Félix Cabello Sánchez and Jésus M. F. Castillo |
| title_full_unstemmed | Banach space techniques underpinning a theory for nearly additive mappings Félix Cabello Sánchez and Jésus M. F. Castillo |
| title_short | Banach space techniques underpinning a theory for nearly additive mappings |
| title_sort | banach space techniques underpinning a theory for nearly additive mappings |
| topic | Banach spaces Mappings (Mathematics) |
| topic_facet | Banach spaces Mappings (Mathematics) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009907760&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
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