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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VerfasserIn: | |
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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Other title: | Frontmatter -- Contents -- Preface -- 1. A primer on ordered vector spaces -- 2. Embeddings, covers, and completions -- 3. Seminorms on pre-Riesz spaces -- 4. Disjointness, bands, and ideals in pre-Riesz spaces -- 5. Operators on pre-Riesz spaces -- Bibliography -- Index |
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Summary: | 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 |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9783110476293 9783110494969 9783110762464 9783110719567 9783110616859 9783110604252 9783110603255 9783110604191 9783110603194 |
ISSN: | 0938-6572 ; |
DOI: | 10.1515/9783110476293 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Anke Kalauch, Onno van Gaans. |