Finite elements in vector lattices:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
2014
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | IX, 220 S. graph. Darst. |
| ISBN: | 3110350777 9783110350777 9783110350791 |
Internformat
MARC
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| 300 | |a IX, 220 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS
1 INTRODUCTION 1
2 ORDERED VECTOR SPACES AND VECTOR LATTICES 4
2.1 ORDERED VECTOR SPACES AND POSITIVE OPERATORS 4
2.2 VECTOR LATTICES 6
2.3 ORDERED NORMED SPACES 11
2.4 NORMED RIESZ
SPACES AND BANACH LATTICES 12
2.5 REPRESENTATION OF BANACH LATTICES 16
3 FINITE, TOTALLY
FINITE AND SELFMAJORIZING
ELEMENTS 18
3.1 FINITE AND TOTALLY FINITE ELEMENTS IN VECTOR LATTICES 18
3.2 FINITE ELEMENTS IN BANACH LATTICES 29
3.3 FINITE ELEMENTS IN SUBLATTICES AND IN DIRECT SUMS OF BANACH
LATTICES 33
3.3.1 FINITE ELEMENTS IN SUBLATTICES 33
3.3.2 FINITE ELEMENTS IN THE BIDUAL OF BANACH
LATTICES 37
3.3.3 FINITE ELEMENTS IN DIRECT SUMS OF BANACH LATTICES 39
3.4 SELFMAJORIZING ELEMENTS IN VECTOR LATTICES 41
3.4.1 THE ORDER
IDEAL OF ALL SELFMAJORIZING ELEMENTS IN A VECTOR LATTICE 42
3.4.2 GENERAL
PROPERTIES OF SELFMAJORIZING ELEMENTS 44
3.4.3 EXAMPLES OF SELFMAJORIZING ELEMENTS 47
3.5 FINITE ELEMENTS IN L-ALGEBRAS AND IN PRODUCT ALGEBRAS 49
3.5.1 LATTICE ORDERED ALGEBRAS 49
3.5.2 FINITE ELEMENTS IN UNITARY L-ALGEBRAS 52
3.5.3 FINITE ELEMENTS IN NONUNITARY /-ALGEBRAS 57
3.5.4 FINITE ELEMENTS IN PRODUCT ALGEBRAS 63
4 FINITE ELEMENTS
IN VECTOR LATTICES
OF LINEAR OPERATORS 69
4.1 SOME GENERAL RESULTS 70
4.2 FINITENESS OF REGULAR OPERATORS ON AL-SPACES 75
4.3 FINITE RANK OPERATORS IN THE VECTOR LATTICE OF REGULAR OPERATORS 77
4.4 SOME VECTOR LATTICES AND BANACH LATTICES OF OPERATORS 81
4.4.1 VECTOR LATTICES OF OPERATORS 83
4.4.2 BANACH LATTICES OF OPERATORS 84
4.5 OPERATORS AS FINITE ELEMENTS 90
4.6 FINITE RANK OPERATORS AS FINITE ELEMENTS 92
4.7 IMPACT OF THE ORDER STRUCTURE OF V(E,F)
ON THE LATTICE PROPERTIES OF
ANDF 96
HTTP://D-NB.INFO/1048116468
VIII *
CONTENTS
5 THE SPACE OF MAXIMAL
IDEALS
OF A
VECTOR LATTICE 100
5.1 REPRESENTATION OF VECTOR LATTICES BY MEANS OF EXTENDED REAL
CONTINUOUS
FUNCTIONS 100
5.2 MAXIMAL IDEALS AND DISCRETE FUNCTIONALS 103
5.3 THE TOPOLOGY ON THE SPACE OF MAXIMAL IDEALS OF A
VECTOR LATTICE 107
5.4 THE HAUSDORFF PROPERTY OF SDT 109
6 TOPOLOGICAL CHARACTERIZATION
OF FINITE ELEMENTS 115
6.1 TOPOLOGICAL CHARACTERIZATION OF FINITE, TOTALLY FINITE AND
SELFMAJORIZING
ELEMENTS 115
6.1.1 THE CANONICAL MAP AND THE CONDITIONAL REPRESENTATION 116
6.1.2 TOPOLOGICAL CHARACTERIZATION OF FINITE ELEMENTS 121
6.1.3 TOPOLOGICAL CHARACTERIZATION OF TOTALLY FINITE ELEMENTS 125
6.1.4 TOPOLOGICAL CHARACTERIZATION OF SELFMAJORIZING ELEMENTS 129
6.2 RELATIONS BETWEEN THE IDEALS OF FINITE, TOTALLY FINITE AND
SELFMAJORIZING
ELEMENTS 131
6.3 THE TOPOLOGICAL SPACE 9JT FOR VECTOR
LATTICES OF TYPE (I) 134
6.4 EXAMPLES 138
7 REPRESENTATIONS OF VECTOR LATTICES
AND THEIR PROPERTIES 144
7.1 A CLASSIFICATION OF REPRESENTATIONS AND THE STANDARD MAP 144
7.2 VECTOR LATTICES OF TYPE (I) AND THEIR REPRESENTATIONS 148
8 VECTOR LATTICES
OF CONTINUOUS FUNCTIONS
WITH FINITE ELEMENTS 157
8.1 VECTOR LATTICES OF CONTINUOUS FUNCTIONS WITH MANY FINITE
FUNCTIONS 157
8.2 FINITE ELEMENTS IN VECTOR LATTICES OF CONTINUOUS FUNCTIONS 162
8.3 AN ISOMORPHISM RESULT FOR VECTOR LATTICES OF CONTINUOUS
FUNCTIONS 167
9 REPRESENTATIONS OF VECTOR LATTICES
BY MEANS
OF CONTINUOUS
FUNCTIONS 171
9.1 REPRESENTATIONS WHICH CONTAIN FINITE FUNCTIONS 171
9.2 THE EXISTENCE OF OA-REPRESENTATIONS FOR VECTOR LATTICES OF
TYPE (E) 177
9.3 IF-VECTOR LATTICES 182
9.4 VECTOR LATTICES OF TYPE (C
M
) 184
10 REPRESENTATIONS OF VECTOR LATTICES
BY MEANS
OF BASES OF FINITE
ELEMENTS 191
10.1 BASES OF FINITE ELEMENTSAND A-REPRESENTATIONS 191
CONTENTS
10.2 REPRESENTATIONS BY MEANS OF FT-BASES OF FINITE ELEMENTS 195
10.3 SOME PROPERTIES OF THE REALIZATION SPACE 199
LIST OF EXAMPLES 207
LIST OF SYMBOLS 209
BIBLIOGRAPHY 211
INDEX 217 |
| any_adam_object | 1 |
| author | Weber, Martin R. |
| author_facet | Weber, Martin R. |
| author_role | aut |
| author_sort | Weber, Martin R. |
| author_variant | m r w mr mrw |
| building | Verbundindex |
| bvnumber | BV041953255 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)872700195 (DE-599)DNB1048116468 |
| dewey-full | 515.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.73 |
| dewey-search | 515.73 |
| dewey-sort | 3515.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041953255 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T01:37:13Z |
| institution | BVB |
| isbn | 3110350777 9783110350777 9783110350791 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027396178 |
| oclc_num | 872700195 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-83 |
| owner_facet | DE-19 DE-BY-UBM DE-83 |
| physical | IX, 220 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | De Gruyter |
| record_format | marc |
| spelling | Weber, Martin R. Verfasser aut Finite elements in vector lattices Martin R. Weber Berlin De Gruyter 2014 IX, 220 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Riesz-Raum (DE-588)4178139-9 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s Riesz-Raum (DE-588)4178139-9 s DE-604 Erscheint auch als Online-Ausgabe 978-3-11-035078-4 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4607421&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027396178&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weber, Martin R. Finite elements in vector lattices Finite-Elemente-Methode (DE-588)4017233-8 gnd Riesz-Raum (DE-588)4178139-9 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4178139-9 |
| title | Finite elements in vector lattices |
| title_auth | Finite elements in vector lattices |
| title_exact_search | Finite elements in vector lattices |
| title_full | Finite elements in vector lattices Martin R. Weber |
| title_fullStr | Finite elements in vector lattices Martin R. Weber |
| title_full_unstemmed | Finite elements in vector lattices Martin R. Weber |
| title_short | Finite elements in vector lattices |
| title_sort | finite elements in vector lattices |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd Riesz-Raum (DE-588)4178139-9 gnd |
| topic_facet | Finite-Elemente-Methode Riesz-Raum |
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