Pre-Riesz Spaces / / Anke Kalauch, Onno van Gaans.
This monograph develops the theory of pre-Riesz spaces, which are the partially ordered vector spaces that embed order densely into Riesz spaces. Concepts from Riesz space theory such as disjointness, ideals, and bands are extended to pre-Riesz spaces. The analysis revolves around embedding techniqu...
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Superior document: | Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2018] ©2019 |
Year of Publication: | 2018 |
Language: | English |
Series: | De Gruyter Expositions in Mathematics ,
66 |
Online Access: | |
Physical Description: | 1 online resource (XIII, 301 p.) |
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100 | 1 | |a Kalauch, Anke, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Pre-Riesz Spaces / |c Anke Kalauch, Onno van Gaans. |
264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2018] | |
264 | 4 | |c ©2019 | |
300 | |a 1 online resource (XIII, 301 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a De Gruyter Expositions in Mathematics , |x 0938-6572 ; |v 66 | |
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t 1. A primer on ordered vector spaces -- |t 2. Embeddings, covers, and completions -- |t 3. Seminorms on pre-Riesz spaces -- |t 4. Disjointness, bands, and ideals in pre-Riesz spaces -- |t 5. Operators on pre-Riesz spaces -- |t Bibliography -- |t Index |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a This monograph develops the theory of pre-Riesz spaces, which are the partially ordered vector spaces that embed order densely into Riesz spaces. Concepts from Riesz space theory such as disjointness, ideals, and bands are extended to pre-Riesz spaces. The analysis revolves around embedding techniques, including the Riesz completion and the functional representation. In the same spirit, norms and topologies on a pre-Riesz space and their extensions to the Riesz completion are examined. The generalized concepts are used to investigate disjointness preserving operators on pre-Riesz spaces and related notions. The monograph presents recent results as well as being an accessible introduction to the theory of partially ordered vector spaces and positive operators. Contents A primer on ordered vector spaces Embeddings, covers, and completions Seminorms on pre-Riesz spaces Disjointness, bands, and ideals in pre-Riesz spaces Operators on pre-Riesz spaces | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) | |
650 | 0 | |a Partially ordered spaces. | |
650 | 0 | |a Riesz spaces. | |
650 | 0 | |a Vector spaces. | |
650 | 4 | |a Funktionalanalysis. | |
650 | 4 | |a Riesz-Raum. | |
650 | 4 | |a Vektorverband. | |
650 | 7 | |a MATHEMATICS / Functional Analysis. |2 bisacsh | |
700 | 1 | |a van Gaans, Onno, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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856 | 4 | 0 | |u https://doi.org/10.1515/9783110476293 |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9783110476293 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9783110476293/original |
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