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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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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DOI: https://doi.org/10.1007/978-3-030-10850-2_15
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