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Main Authors:	Kalauch, Anke 1972- (Author), van Gaans, Onno (Author)
Format:	Book
Language:	English
Published:	Berlin ; Boston De Gruyter [2019]
Series:	De Gruyter expositions in mathematics Volume 66
Subjects:	Vektorverband Riesz-Raum Halbgeordneter Vektorraum Funktionalanalysis
Online Access:	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110475395&searchTitles=true Inhaltsverzeichnis
Physical Description:	XIII,301 Seiten Illustrationen 24 cm x 17 cm
ISBN:	9783110475395 3110475391

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MARC


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Record in the Search Index

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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
author_GND	(DE-588)123832659
author_facet	Kalauch, Anke 1972- van Gaans, Onno
author_role	aut aut
author_sort	Kalauch, Anke 1972-
author_variant	a k ak g o v go gov
building	Verbundindex
bvnumber	BV045283980
classification_rvk	SK 600
ctrlnum	(OCoLC)1077492270 (DE-599)DNB1152831194
discipline	Mathematik
format	Book
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language	English
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owner	DE-20 DE-11
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physical	XIII,301 Seiten Illustrationen 24 cm x 17 cm
publishDate	2019
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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
url	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110475395&searchTitles=true 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
volume_link	(DE-604)BV004069300
work_keys_str_mv	AT kalauchanke prerieszspaces AT vangaansonno prerieszspaces

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