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Multiplier Convergent Series

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Title: Multiplier Convergent Series
Description: If λ is a space of scalar-valued sequences, then a series ∑j xj in a topological vector space X is λ-multiplier convergent if the series ∑j=1∞ tjxj converges in X for every {tj} ελ. This monograph studies properties of such series and gives applications to topics in locally convex spaces and vector-valued measures. A number of versions of the Orlicz-Pettis theorem are derived for multiplier convergent series with respect to various locally convex topologies. Variants of the classical Hahn-Schur theorem on the equivalence of weak and norm convergent series in ι1 are also developed for multiplier convergent series. Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.
Authors: Charles W Swartz
Resource Type: eBook.
Subjects: Series, Arithmetic, Orlicz spaces, Convergence, Multipliers (Mathematical analysis)
Categories: MATHEMATICS / Differential Equations / General, MATHEMATICS / Vector Analysis, MATHEMATICS / Mathematical Analysis
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 305214
RelevancyScore: 1025
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1024.62744140625
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  Label: Title
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  Data: Multiplier Convergent Series
– Name: Abstract
  Label: Description
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  Data: If λ is a space of scalar-valued sequences, then a series ∑j xj in a topological vector space X is λ-multiplier convergent if the series ∑j=1∞ tjxj converges in X for every {tj} ελ. This monograph studies properties of such series and gives applications to topics in locally convex spaces and vector-valued measures. A number of versions of the Orlicz-Pettis theorem are derived for multiplier convergent series with respect to various locally convex topologies. Variants of the classical Hahn-Schur theorem on the equivalence of weak and norm convergent series in ι1 are also developed for multiplier convergent series. Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.
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  Data: <searchLink fieldCode="AR" term="%22Charles+W+Swartz%22">Charles W Swartz</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Series%2C+Arithmetic%22">Series, Arithmetic</searchLink><br /><searchLink fieldCode="DE" term="%22Orlicz+spaces%22">Orlicz spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Convergence%22">Convergence</searchLink><br /><searchLink fieldCode="DE" term="%22Multipliers+%28Mathematical+analysis%29%22">Multipliers (Mathematical analysis)</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 515.243
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Series, Arithmetic
        Type: general
      – SubjectFull: Orlicz spaces
        Type: general
      – SubjectFull: Convergence
        Type: general
      – SubjectFull: Multipliers (Mathematical analysis)
        Type: general
    Titles:
      – TitleFull: Multiplier Convergent Series
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Charles W Swartz
      – PersonEntity:
          Name:
            NameFull: Charles W Swartz
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2009
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9789812833877
            – Type: isbn-electronic
              Value: 9789812833884
          Titles:
            – TitleFull: Multiplier Convergent Series
              Type: main
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