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Dedekind Complete and Order Continuous Banach C(K)-Modules

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Positivity and Noncommutative Analysis

Part of the book series: Trends in Mathematics ((TM))

Abstract

We extend the notions of Dedekind complete and σ-Dedekind complete Banach lattices to Banach C(K)-modules. As our main result we prove for these modules an analogue of Lozanovsky’s well-known characterization of Banach lattices with order continuous norm.

This paper is dedicated to our dear friend, Professor Ben de Pagter, on the occasion of his 65th birthday

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Author information

Authors and Affiliations

  1. Department of Mathematics, Community College of Philadelphia, Philadelphia, PA, USA

    Arkady Kitover

  2. Department of Mathematics and Statistics, University of New Hampshire, Durham, NH, USA

    Mehmet Orhon

Authors
  1. Arkady Kitover
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  2. Mehmet Orhon
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Corresponding author

Correspondence to Arkady Kitover .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Mississippi, Oxford, MS, USA

    Gerard Buskes

  2. Mathematical Institute, Leiden University, Leiden, The Netherlands; Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

    Marcel de Jeu

  3. College of Science and Engineering, Flinders University, Adelaide, Australia

    Peter Dodds

  4. Department of Mathematics, University of South Carolina, Columbia, SC, USA

    Anton Schep

  5. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Fedor Sukochev

  6. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Jan van Neerven

  7. Mathematical Sciences Research Centre, Queen’s University Belfast, Belfast, UK

    Anthony Wickstead

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Kitover, A., Orhon, M. (2019). Dedekind Complete and Order Continuous Banach C(K)-Modules. In: Buskes, G., et al. Positivity and Noncommutative Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-10850-2_15

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