Banach Lattices and Positive Operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1974
|
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften
215 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Vector lattices-also called Riesz spaces, K-lineals, or linear lattices-were first considered by F. Riesz, L. Kantorovic, and H. Freudenthal in the middle nineteen thirties; thus their early theory dates back almost as far as the beginning of the systematic investigation of Banach spaces. Schools of research on vector lattices were subsequently founded in the Soviet Union (Kantorovic, Judin, Pinsker, Vulikh) and in Japan (Nakano, Ogasawara, Yosida); other important contributions came from the United States (G. Birkhoff, Kakutani, M. H. Stone). L. Kantorovic and his school first recognized the importance of studying vector lattices in connection with Banach's theory of normed vector spaces; they investigated normed vector lattices as well as order-related linear operators between such vector lattices. (Cf. Kantorovic-Vulikh-Pinsker [1950] and Vulikh [1967].) However, in the years following that early period, functional analysis and vector lattice theory began drifting more and more apart; it is my impression that "linear order theory" could not quite keep pace with the rapid development of general functional analysis and thus developed into a theory largely existing for its own sake, even though it had interesting and beautiful applications here and there |
| Beschreibung: | 1 Online-Ressource (XII, 378 p) |
| ISBN: | 9783642659706 9783642659720 |
| DOI: | 10.1007/978-3-642-65970-6 |
Internformat
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| 490 | 1 | |a Die Grundlehren der mathematischen Wissenschaften |v 215 | |
| 500 | |a Vector lattices-also called Riesz spaces, K-lineals, or linear lattices-were first considered by F. Riesz, L. Kantorovic, and H. Freudenthal in the middle nineteen thirties; thus their early theory dates back almost as far as the beginning of the systematic investigation of Banach spaces. Schools of research on vector lattices were subsequently founded in the Soviet Union (Kantorovic, Judin, Pinsker, Vulikh) and in Japan (Nakano, Ogasawara, Yosida); other important contributions came from the United States (G. Birkhoff, Kakutani, M. H. Stone). L. Kantorovic and his school first recognized the importance of studying vector lattices in connection with Banach's theory of normed vector spaces; they investigated normed vector lattices as well as order-related linear operators between such vector lattices. (Cf. Kantorovic-Vulikh-Pinsker [1950] and Vulikh [1967].) However, in the years following that early period, functional analysis and vector lattice theory began drifting more and more apart; it is my impression that "linear order theory" could not quite keep pace with the rapid development of general functional analysis and thus developed into a theory largely existing for its own sake, even though it had interesting and beautiful applications here and there | ||
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Datensatz im Suchindex
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| author | Schaefer, Helmut H. |
| author_facet | Schaefer, Helmut H. |
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| author_sort | Schaefer, Helmut H. |
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| bvnumber | BV042422894 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863790233 (DE-599)BVBBV042422894 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-65970-6 |
| format | Electronic eBook |
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| id | DE-604.BV042422894 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:38:45Z |
| institution | BVB |
| isbn | 9783642659706 9783642659720 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858311 |
| oclc_num | 863790233 |
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| physical | 1 Online-Ressource (XII, 378 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series | Die Grundlehren der mathematischen Wissenschaften |
| series2 | Die Grundlehren der mathematischen Wissenschaften |
| spelling | Schaefer, Helmut H. Verfasser aut Banach Lattices and Positive Operators by Helmut H. Schaefer Berlin, Heidelberg Springer Berlin Heidelberg 1974 1 Online-Ressource (XII, 378 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften 215 Vector lattices-also called Riesz spaces, K-lineals, or linear lattices-were first considered by F. Riesz, L. Kantorovic, and H. Freudenthal in the middle nineteen thirties; thus their early theory dates back almost as far as the beginning of the systematic investigation of Banach spaces. Schools of research on vector lattices were subsequently founded in the Soviet Union (Kantorovic, Judin, Pinsker, Vulikh) and in Japan (Nakano, Ogasawara, Yosida); other important contributions came from the United States (G. Birkhoff, Kakutani, M. H. Stone). L. Kantorovic and his school first recognized the importance of studying vector lattices in connection with Banach's theory of normed vector spaces; they investigated normed vector lattices as well as order-related linear operators between such vector lattices. (Cf. Kantorovic-Vulikh-Pinsker [1950] and Vulikh [1967].) However, in the years following that early period, functional analysis and vector lattice theory began drifting more and more apart; it is my impression that "linear order theory" could not quite keep pace with the rapid development of general functional analysis and thus developed into a theory largely existing for its own sake, even though it had interesting and beautiful applications here and there Mathematics Mathematics, general Mathematik Vektorraum (DE-588)4130622-3 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Banach-Verband (DE-588)4273753-9 gnd rswk-swf Positiver Operator (DE-588)4046876-8 gnd rswk-swf Positiver Operator (DE-588)4046876-8 s Banach-Verband (DE-588)4273753-9 s 1\p DE-604 Vektorraum (DE-588)4130622-3 s 2\p DE-604 Operator (DE-588)4130529-2 s 3\p DE-604 Die Grundlehren der mathematischen Wissenschaften 215 (DE-604)BV049758308 215 https://doi.org/10.1007/978-3-642-65970-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schaefer, Helmut H. Banach Lattices and Positive Operators Die Grundlehren der mathematischen Wissenschaften Mathematics Mathematics, general Mathematik Vektorraum (DE-588)4130622-3 gnd Operator (DE-588)4130529-2 gnd Banach-Verband (DE-588)4273753-9 gnd Positiver Operator (DE-588)4046876-8 gnd |
| subject_GND | (DE-588)4130622-3 (DE-588)4130529-2 (DE-588)4273753-9 (DE-588)4046876-8 |
| title | Banach Lattices and Positive Operators |
| title_auth | Banach Lattices and Positive Operators |
| title_exact_search | Banach Lattices and Positive Operators |
| title_full | Banach Lattices and Positive Operators by Helmut H. Schaefer |
| title_fullStr | Banach Lattices and Positive Operators by Helmut H. Schaefer |
| title_full_unstemmed | Banach Lattices and Positive Operators by Helmut H. Schaefer |
| title_short | Banach Lattices and Positive Operators |
| title_sort | banach lattices and positive operators |
| topic | Mathematics Mathematics, general Mathematik Vektorraum (DE-588)4130622-3 gnd Operator (DE-588)4130529-2 gnd Banach-Verband (DE-588)4273753-9 gnd Positiver Operator (DE-588)4046876-8 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Vektorraum Operator Banach-Verband Positiver Operator |
| url | https://doi.org/10.1007/978-3-642-65970-6 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT schaeferhelmuth banachlatticesandpositiveoperators |