Inverses and regularity of disjointness preserving operators:
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Warszawa
Inst. Matematyczny PAN
2005
|
| Schriftenreihe: | Dissertationes mathematicae
433 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 48 S. |
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MARC
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Datensatz im Suchindex
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| adam_text | Titel: Inverses and regularity of disjointness preserving operators
Autor: Abramovich, Yuri A
Jahr: 2005
CONTENTS
1. Introduction....................................................................................................................................................5
2. Basic definitions, notations, and auxiliary results............................................................................6
2.1. Krein-Kakutani representation and related properties of vector lattices........................7
2.2. Vector lattices with some degree of lateral completeness......................................................8
2.3. Disjointness preserving operators..................................................................................................11
2.4. d-dimension and d-independence....................................................................................................12
2.5. Condition fh............................................................................................................................................14
2.6. The Luxemburg condition................................................................................................................17
3. d-universal domains......................................................................................................................................22
3.1. Domains on which each disjointness preserving operator is regular..................................22
3.2. Domains on which x X z Tx XTz for each injective disjointness preserving ope-
rator T......................................................................................................................................................23
4. d-rigid vector lattices. General case........................................................................................................25
5. Weakly co-complete domains....................................................................................................................27
5.1. The main results..................................................................................................................................27
5.2. Proofs of Theorems 5.1.1 and 5.1.3................................................................................................30
5.3. Proofs of Theorems 5.1.4 and 5.1.5................................................................................................34
6. Weakly co-complete domains with the projection property or with the countable sup
property............................................................................................................................................................36
6.1. The general case....................................................................................................................................36
6.2. Dedekind complete domains. Relatively uniformly complete domains with the count-
able sup property..................................................................................................................................38
7. Huijsmans-de Pagter-Koldunov theorem............................................................................................40
7.1. The HPK-theorem. Some improvements....................................................................................40
7.2. The case when the range Y is countably normed....................................................................42
7.3. Range-domain interchange in the HPK-theorem......................................................................44
8. Applications to spaces of continuous functions..................................................................................46
References..............................................................................................................................................................47
2000 Mathematics Subject Classification: Primary 47B60, 47B65, 47B38, 46A40, 46B40, 46B42;
Secondary 54G05.
Received 12.1.2005.
[3]
|
| adam_txt |
Titel: Inverses and regularity of disjointness preserving operators
Autor: Abramovich, Yuri A
Jahr: 2005
CONTENTS
1. Introduction.5
2. Basic definitions, notations, and auxiliary results.6
2.1. Krein-Kakutani representation and related properties of vector lattices.7
2.2. Vector lattices with some degree of lateral completeness.8
2.3. Disjointness preserving operators.11
2.4. d-dimension and d-independence.12
2.5. Condition fh.14
2.6. The Luxemburg condition.17
3. d-universal domains.22
3.1. Domains on which each disjointness preserving operator is regular.22
3.2. Domains on which x X z Tx XTz for each injective disjointness preserving ope-
rator T.23
4. d-rigid vector lattices. General case.25
5. Weakly co-complete domains.27
5.1. The main results.27
5.2. Proofs of Theorems 5.1.1 and 5.1.3.30
5.3. Proofs of Theorems 5.1.4 and 5.1.5.34
6. Weakly co-complete domains with the projection property or with the countable sup
property.36
6.1. The general case.36
6.2. Dedekind complete domains. Relatively uniformly complete domains with the count-
able sup property.38
7. Huijsmans-de Pagter-Koldunov theorem.40
7.1. The HPK-theorem. Some improvements.40
7.2. The case when the range Y is countably normed.42
7.3. Range-domain interchange in the HPK-theorem.44
8. Applications to spaces of continuous functions.46
References.47
2000 Mathematics Subject Classification: Primary 47B60, 47B65, 47B38, 46A40, 46B40, 46B42;
Secondary 54G05.
Received 12.1.2005.
[3] |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:05:02Z |
| indexdate | 2024-07-09T20:36:09Z |
| institution | BVB |
| language | English |
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| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Abramovich, Yuri A. 1945-2003 Verfasser (DE-588)120117967 aut Inverses and regularity of disjointness preserving operators Y. A. Abramovich ; A. K. Kitover Warszawa Inst. Matematyczny PAN 2005 48 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 433 Banach-Verband (DE-588)4273753-9 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Banach-Verband (DE-588)4273753-9 s Operatortheorie (DE-588)4075665-8 s DE-604 Kitover, A. K. Verfasser (DE-588)1294248286 aut Dissertationes mathematicae 433 (DE-604)BV000003039 433 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014665127&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abramovich, Yuri A. 1945-2003 Kitover, A. K. Inverses and regularity of disjointness preserving operators Dissertationes mathematicae Banach-Verband (DE-588)4273753-9 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4273753-9 (DE-588)4075665-8 |
| title | Inverses and regularity of disjointness preserving operators |
| title_auth | Inverses and regularity of disjointness preserving operators |
| title_exact_search | Inverses and regularity of disjointness preserving operators |
| title_exact_search_txtP | Inverses and regularity of disjointness preserving operators |
| title_full | Inverses and regularity of disjointness preserving operators Y. A. Abramovich ; A. K. Kitover |
| title_fullStr | Inverses and regularity of disjointness preserving operators Y. A. Abramovich ; A. K. Kitover |
| title_full_unstemmed | Inverses and regularity of disjointness preserving operators Y. A. Abramovich ; A. K. Kitover |
| title_short | Inverses and regularity of disjointness preserving operators |
| title_sort | inverses and regularity of disjointness preserving operators |
| topic | Banach-Verband (DE-588)4273753-9 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Banach-Verband Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014665127&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
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