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

  • Arkady KitoverEmail author
  • Mehmet Orhon
Chapter
Part of the Trends in Mathematics book series (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.

Keywords

Banach lattice Dedekind complete Order continuous Banach C(K)-module 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsCommunity College of PhiladelphiaPhiladelphiaUSA
  2. 2.Department of Mathematics and StatisticsUniversity of New HampshireDurhamUSA

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