Dominated Operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2000
|
| Schriftenreihe: | Mathematics and Its Applications
519 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The notion of a dominated or rnajorized operator rests on a simple idea that goes as far back as the Cauchy method of majorants. Loosely speaking, the idea can be expressed as follows. If an operator (equation) under study is dominated by another operator (equation), called a dominant or majorant, then the properties of the latter have a substantial influence on the properties of the former . Thus, operators or equations that have "nice" dominants must possess "nice" properties. In other words, an operator with a somehow qualified dominant must be qualified itself. Mathematical tools, putting the idea of domination into a natural and complete form, were suggested by L. V. Kantorovich in 1935-36. He introduced the funda mental notion of a vector space normed by elements of a vector lattice and that of a linear operator between such spaces which is dominated by a positive linear or monotone sublinear operator. He also applied these notions to solving functional equations. In the succeedingyears many authors studied various particular cases of lattice normed spaces and different classes of dominated operators. However, research was performed within and in the spirit of the theory of vector and normed lattices. So, it is not an exaggeration to say that dominated operators, as independent objects of investigation, were beyond the reach of specialists for half a century. As a consequence, the most important structural properties and some interesting applications of dominated operators have become available since recently |
| Beschreibung: | 1 Online-Ressource (XIV, 446 p) |
| ISBN: | 9789401593496 9789048155286 |
| DOI: | 10.1007/978-94-015-9349-6 |
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| 500 | |a The notion of a dominated or rnajorized operator rests on a simple idea that goes as far back as the Cauchy method of majorants. Loosely speaking, the idea can be expressed as follows. If an operator (equation) under study is dominated by another operator (equation), called a dominant or majorant, then the properties of the latter have a substantial influence on the properties of the former . Thus, operators or equations that have "nice" dominants must possess "nice" properties. In other words, an operator with a somehow qualified dominant must be qualified itself. Mathematical tools, putting the idea of domination into a natural and complete form, were suggested by L. V. Kantorovich in 1935-36. He introduced the funda mental notion of a vector space normed by elements of a vector lattice and that of a linear operator between such spaces which is dominated by a positive linear or monotone sublinear operator. He also applied these notions to solving functional equations. In the succeedingyears many authors studied various particular cases of lattice normed spaces and different classes of dominated operators. However, research was performed within and in the spirit of the theory of vector and normed lattices. So, it is not an exaggeration to say that dominated operators, as independent objects of investigation, were beyond the reach of specialists for half a century. As a consequence, the most important structural properties and some interesting applications of dominated operators have become available since recently | ||
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Datensatz im Suchindex
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| author | Kusraev, Anatoly G. |
| author_facet | Kusraev, Anatoly G. |
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| author_sort | Kusraev, Anatoly G. |
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| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9349-6 |
| format | Electronic eBook |
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| id | DE-604.BV042424134 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401593496 9789048155286 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859551 |
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| physical | 1 Online-Ressource (XIV, 446 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2000 |
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| publisher | Springer Netherlands |
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| spelling | Kusraev, Anatoly G. Verfasser aut Dominated Operators by Anatoly G. Kusraev Dordrecht Springer Netherlands 2000 1 Online-Ressource (XIV, 446 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 519 The notion of a dominated or rnajorized operator rests on a simple idea that goes as far back as the Cauchy method of majorants. Loosely speaking, the idea can be expressed as follows. If an operator (equation) under study is dominated by another operator (equation), called a dominant or majorant, then the properties of the latter have a substantial influence on the properties of the former . Thus, operators or equations that have "nice" dominants must possess "nice" properties. In other words, an operator with a somehow qualified dominant must be qualified itself. Mathematical tools, putting the idea of domination into a natural and complete form, were suggested by L. V. Kantorovich in 1935-36. He introduced the funda mental notion of a vector space normed by elements of a vector lattice and that of a linear operator between such spaces which is dominated by a positive linear or monotone sublinear operator. He also applied these notions to solving functional equations. In the succeedingyears many authors studied various particular cases of lattice normed spaces and different classes of dominated operators. However, research was performed within and in the spirit of the theory of vector and normed lattices. So, it is not an exaggeration to say that dominated operators, as independent objects of investigation, were beyond the reach of specialists for half a century. As a consequence, the most important structural properties and some interesting applications of dominated operators have become available since recently Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Functional Analysis Operator Theory Measure and Integration Mathematical Logic and Foundations Mathematik Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s 1\p DE-604 https://doi.org/10.1007/978-94-015-9349-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kusraev, Anatoly G. Dominated Operators Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Functional Analysis Operator Theory Measure and Integration Mathematical Logic and Foundations Mathematik Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4075665-8 |
| title | Dominated Operators |
| title_auth | Dominated Operators |
| title_exact_search | Dominated Operators |
| title_full | Dominated Operators by Anatoly G. Kusraev |
| title_fullStr | Dominated Operators by Anatoly G. Kusraev |
| title_full_unstemmed | Dominated Operators by Anatoly G. Kusraev |
| title_short | Dominated Operators |
| title_sort | dominated operators |
| topic | Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Functional Analysis Operator Theory Measure and Integration Mathematical Logic and Foundations Mathematik Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Functional Analysis Operator Theory Measure and Integration Mathematical Logic and Foundations Mathematik Operatortheorie |
| url | https://doi.org/10.1007/978-94-015-9349-6 |
| work_keys_str_mv | AT kusraevanatolyg dominatedoperators |