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Pre-Riesz Spaces

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Title: Pre-Riesz Spaces
Description: 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
Authors: Anke Kalauch, Onno van Gaans
Resource Type: eBook.
Subjects: Partially ordered spaces, Riesz spaces, Vector spaces
Categories: MATHEMATICS / Functional Analysis, MATHEMATICS / Mathematical Analysis
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
  – Type: ebook-epub
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 1949447
RelevancyScore: 1090
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1090.09973144531
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Pre-Riesz Spaces
– Name: Abstract
  Label: Description
  Group: Ab
  Data: 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
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Anke+Kalauch%22">Anke Kalauch</searchLink><br /><searchLink fieldCode="AR" term="%22Onno+van+Gaans%22">Onno van Gaans</searchLink>
– Name: TypePub
  Label: Resource Type
  Group: TypPub
  Data: eBook.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Partially+ordered+spaces%22">Partially ordered spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Riesz+spaces%22">Riesz spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+spaces%22">Vector spaces</searchLink>
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  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Functional+Analysis%22">MATHEMATICS / Functional Analysis</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Mathematical+Analysis%22">MATHEMATICS / Mathematical Analysis</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 515.73
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Partially ordered spaces
        Type: general
      – SubjectFull: Riesz spaces
        Type: general
      – SubjectFull: Vector spaces
        Type: general
    Titles:
      – TitleFull: Pre-Riesz Spaces
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Anke Kalauch
      – PersonEntity:
          Name:
            NameFull: Onno van Gaans
      – PersonEntity:
          Name:
            NameFull: Anke Kalauch
      – PersonEntity:
          Name:
            NameFull: Onno van Gaans
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2019
            – D: 15
              M: 01
              Type: profile
              Y: 2019
          Identifiers:
            – Type: isbn-print
              Value: 9783110475395
            – Type: isbn-electronic
              Value: 9783110475449
            – Type: isbn-electronic
              Value: 9783110476293
          Numbering:
            – Type: volume
              Value: 00066
          Titles:
            – TitleFull: Pre-Riesz Spaces
              Type: main
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