Pre-Riesz spaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2019]
|
| Schriftenreihe: | De Gruyter expositions in mathematics
Volume 66 |
| Schlagworte: | |
| Online-Zugang: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110475395&searchTitles=true Inhaltsverzeichnis |
| Beschreibung: | XIII,301 Seiten Illustrationen 24 cm x 17 cm |
| ISBN: | 9783110475395 3110475391 |
Internformat
MARC
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| 264 | 4 | |c © 2019 | |
| 300 | |a XIII,301 Seiten |b Illustrationen |c 24 cm x 17 cm | ||
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| 653 | |a Vektorverband | ||
| 653 | |a Funktionalanalysis | ||
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Datensatz im Suchindex
| _version_ | 1804179060197163008 |
|---|---|
| adam_text | CONTENTS
PREFACE * IX
1 A PRIMER ON ORDERED VECTOR SPACES * 1
1.1 ORDERED VECTOR SPACES * 2
1.1.1 VECTOR SPACE ORDERS AND CONES * 2
1.1.2 VECTOR LATTICES * 6
1.1.3 THE RIESZ DECOMPOSITION PROPERTY * 8
1.1.4 ORDER CONVERGENCE * 11
1.2 OPERATORS ON ORDERED VECTOR SPACES * 12
1.2.1 ORDER-BOUNDED AND REGULAR OPERATORS * 12
1.2.2 THE RIESZ-KANTOROVICH FORMULAS * 15
1.3 IDEALS AND BANDS IN VECTOR LATTICES * 17
1.3.1 DEFINITIONS AND BASIC PROPERTIES * 17
1.3.2 IDEALSAND BANDS IN C(Q) * 20
1.4 RIESZ HOMOMORPHISMS AND DISJOINTNESS PRESERVING OPERATORS
IN VECTOR LATTICES * 22
1.5 NORM AND ORDER* 26
1.5.1 CLOSED CONES * 27
1.5.2 SEMIMONOTONE NORMS * 28
1.5.3 ORDER UNIT SPACES * 29
1.5.4 NORMED VECTOR LATTICES * 35
1.5.5 RELATIVELY UNIFORM CONVERGENCE * 36
1.6 ORDER DENSENESS * 40
1.7 EXAMPLES * 42
1.7.1 THE ICE CREAM CONE AND FRIENDS * 42
1.7.2 POLYHEDRAL CONES * 46
1.8 ODDS AND ENDS FROM FUNCTIONAL ANALYSIS AND TOPOLOGY * 50
2 EMBEDDINGS, COVERS, AND COMPLETIONS * 53
2.1 DEDEKIND COMPLETION * 54
2.1.1 DEDEKIND CUTS * 54
2.1.2 ADDITION AND SCALAR MULTIPLICATION ON THE SET OF DEDEKIND CUTS
2.1.3 THE DEDEKIND COMPLETION OF AN ARCHIMEDEAN SPACE * 61
2.2 PRE-RIESZ SPACES * 68
2.2.1 DEFINITION AND BASIC PROPERTIES * 68
2.2.2 SOME LATTICE-LIKE FORMULAS * 71
2.3 RIESZ* HOMOMORPHISMS * 74
2.3.1 DEFINITION AND BASIC PROPERTIES * 74
2.3.2 EXTENSION AND RESTRICTION * 76
2.3.3 COMPARISON WITH RIESZ HOMOMORPHISMS * 80
2.4 VECTOR LATTICE COVER AND RIESZ COMPLETION * 87
2.5 FUNCTIONAL REPRESENTATION * 94
2.6 EXAMPLES OF VECTOR LATTICE COVERS * 101
2.6.1 POLYHEDRAL CONES * 102
2.6.2 LORENTZ CONES * 103
2.6.3 POSITIVE SEMIDEFINITE MATRICES * 104
2.6.4 FINITE DIMENSIONAL EXAMPLES BY MEANS OF A DUAL BASE * 107
2.7 THE FREMLIN TENSOR PRODUCT AS RIESZ COMPLETION * 108
2.7.1 THE VECTOR SPACE TENSOR PRODUCT* 108
2.7.2 THE FREMLIN TENSOR PRODUCT* 110
2.7.3 THE PROJECTIVE CONE AND ITS RELATIVELY UNIFORM CLOSURE * 111
2.8 EXTENSION AND RESTRICTION METHOD * 115
3 SEMINORMS ON PRE-RIESZ SPACES * 119
3.1 BASIC PROPERTIES OF SEMINORMS * 119
3.2 PRE-RIESZ SEMINORMS * 121
3.2.1 GENERALIZATION OF RIESZ SEMINORMS: PLAN OF ATTACK * 121
3.2.2 SOLID S E TS
----
123
3.2.3 SOLVEX SETS * 128
3.2.4 PRE-RIESZ SEMINORMS: SEMINORMS WITH SOLVEX UNIT BALLS * 132
3.3 EXTENSION AND RESTRICTION OF MONOTONE SEMINORMS * 138
3.3.1 MONOTONE SEMINORMS AND RELATED CONCEPTS * 139
3.3.2 EXTENSION OF SEMINORMS * 144
3.3.3 EXTENSION AND NORM COMPLETENESS * 150
3.3.4 UNIQUENESS OF EXTENSIONS * 153
3.3.5 QUOTIENTS OVER KERNELS OF MONOTONE SEMINORMS * 157
3.3.6 EXTENSION TO M-SEMINORMS AND L-SEMINORMS * 160
3.4 REGULAR SEMINORMS * 163
3.4.1 DEFINITION AND EXAMPLES * 164
3.4.2 EXTENSION OF REGULAR SEMINORMS * 165
3.4.3 REGULARIZATION OF SEMINORMS * 168
3.5 SEMIMONOTONE NORMS REVISITED * 171
3.6 TOPOLOGIES ON PRE-RIESZ SPACES * 173
3.6.1 LOCALLY FULL TOPOLOGIES
----
174
3.6.2 TOPOLOGIES SUCH THAT THE POSITIVE CONE IS CLOSED * 179
3.6.3 LOCALLY SOLID TOPOLOGIES * 180
3.7 ORDER CONVERGENCE AND UNBOUNDED ORDER CONVERGENCE * 183
3.7.1 ORDER CONVERGENCE REVISITED * 184
3.7.2 EXTENSION AND RESTRICTION OF ORDER CONVERGENCE * 187
3.7.3 UNBOUNDED ORDER CONVERGENCE * 190
4
4.1
4.1.1
4.1.2
4.1.3
4.1.4
4.1.5
4.2
4.2.1
4.2.2
4.2.3
4.3
4.3.1
4.3.2
4.3.3
4.4
4.4.1
4.4.2
4.4.3
4.4.4
4.4.5
5
5.1
5.1.1
5
.
1.2
5.2
5
.
2.1
5.2.2
5.2.3
5.2.4
5.3
5.4
5.4.1
5.4.2
5.4.3
5.5
5.5.1
DISJOINTNESS, BANDS, AND IDEALS IN PRE-RIESZ SPACES * 193
DISJOINTNESS
----
193
DISJOINTNESS IN PARTIALLY ORDERED VECTOR SPACES * 193
DISJOINTNESS AND EMBEDDING * 195
DISJOINTNESS IN SPACES WITH THE RIESZ DECOMPOSITION
PROPERTY
----
196
DISJOINTNESS IN ANTILATTICES
----
198
FORDABLE PRE-RIESZ SPACES * 200
BANDS
----
203
BANDS IN PRE-RIESZ SPACES * 204
EXTENSION OF BANDS
----
204
RESTRICTION OF BANDS IN FORDABLE PRE-RIESZ SPACES * 206
IDEALS
----
206
IDEALS IN PARTIALLY ORDERED VECTOR SPACES * 207
EXTENSION AND RESTRICTION OF IDEALS * 209
DIRECTED IDEALS * 215
BANDS IN SPACES WITH ORDER UNITS * 219
CARRIERS OF BANDS * 219
CHARACTERIZATION OF BANDS BY BISATURATED SETS * 222
BANDS IN SPACES WITH POLYHEDRAL CONES
----
225
BANDS IN FINITE DIMENSIONAL SPACES * 228
CARRIERS OF EXTENSION BANDS * 234
OPERATORS ON PRE-RIESZ SPACES * 237
DISJOINTNESS PRESERVING OPERATORS * 237
DEFINITIONS AND EXAMPLES * 237
RIESZ* HOMOMORPHISMS ON PRE-RIESZ SPACES OF
CONTINUOUS FUNCTIONS
----
243
DISJOINTNESS PRESERVING INVERSE * 247
INVERSES OF BIJECTIVE RIESZ* HOMOMORPHISMS * 247
ON D-ISOMORPHISMS IN PRE-RIESZ SPACES
----
250
DISJOINTNESS PRESERVING BIJECTIONS IN FINITE DIMENSIONS * 252
DISJOINTNESS PRESERVING INVERSE IN INFINITE DIMENSIONS
----
254
DISJOINTNESS PRESERVING CO-SEMIGROUPS * 256
SPACES OF OPERATORS * 261
OPERATORS BETWEEN ORDERED NORMED SPACES * 262
OPERATORS WITH DEDEKIND COMPLETE RANGE SPACES * 264
THE SPACE OF ORDER CONTINUOUS OPERATORS: AN EXAMPLE *
SPECTRAL THEORY FOR OPERATORS ON ORDERED BANACH SPACES
----
DEFINITIONS AND BASIC PROPERTIES * 279
5.5.2
5.5.3
BIBLIOGRAPHY -
INDEX * 297
SPECTRAL PROPERTIES OF POSITIVE OPERATORS * 281
SOME SPECTRAL PROPERTIES FOR OPERATORS ON BANACH LATTICES * 286
* 289
|
| any_adam_object | 1 |
| author | Kalauch, Anke 1972- van Gaans, Onno |
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| author_facet | Kalauch, Anke 1972- van Gaans, Onno |
| author_role | aut aut |
| author_sort | Kalauch, Anke 1972- |
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| building | Verbundindex |
| bvnumber | BV045283980 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)1077492270 (DE-599)DNB1152831194 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV045283980 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:13:51Z |
| institution | BVB |
| isbn | 9783110475395 3110475391 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030671487 |
| oclc_num | 1077492270 |
| open_access_boolean | |
| owner | DE-20 DE-11 |
| owner_facet | DE-20 DE-11 |
| physical | XIII,301 Seiten Illustrationen 24 cm x 17 cm |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Kalauch, Anke 1972- Verfasser (DE-588)123832659 aut Pre-Riesz spaces Anke Kalauch, Onno van Gaans Berlin ; Boston De Gruyter [2019] © 2019 XIII,301 Seiten Illustrationen 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics Volume 66 Vektorverband (DE-588)4187471-7 gnd rswk-swf Riesz-Raum (DE-588)4178139-9 gnd rswk-swf Halbgeordneter Vektorraum (DE-588)4158788-1 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Riesz-Raum Vektorverband Funktionalanalysis Riesz-Raum (DE-588)4178139-9 s Vektorverband (DE-588)4187471-7 s Halbgeordneter Vektorraum (DE-588)4158788-1 s Funktionalanalysis (DE-588)4018916-8 s DE-604 van Gaans, Onno Verfasser aut Erscheint auch als Online-Ausgabe, PDF 978-3-11-047629-3 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-047544-9 De Gruyter expositions in mathematics Volume 66 (DE-604)BV004069300 66 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110475395&searchTitles=true DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030671487&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kalauch, Anke 1972- van Gaans, Onno Pre-Riesz spaces De Gruyter expositions in mathematics Vektorverband (DE-588)4187471-7 gnd Riesz-Raum (DE-588)4178139-9 gnd Halbgeordneter Vektorraum (DE-588)4158788-1 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4187471-7 (DE-588)4178139-9 (DE-588)4158788-1 (DE-588)4018916-8 |
| title | Pre-Riesz spaces |
| title_auth | Pre-Riesz spaces |
| title_exact_search | Pre-Riesz spaces |
| title_full | Pre-Riesz spaces Anke Kalauch, Onno van Gaans |
| title_fullStr | Pre-Riesz spaces Anke Kalauch, Onno van Gaans |
| title_full_unstemmed | Pre-Riesz spaces Anke Kalauch, Onno van Gaans |
| title_short | Pre-Riesz spaces |
| title_sort | pre riesz spaces |
| topic | Vektorverband (DE-588)4187471-7 gnd Riesz-Raum (DE-588)4178139-9 gnd Halbgeordneter Vektorraum (DE-588)4158788-1 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Vektorverband Riesz-Raum Halbgeordneter Vektorraum Funktionalanalysis |
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