A Remark on the Representation of Vector Lattices as Spaces of Continuous Real-Valued Functions

Yuri A. Abramovich and Wolfgang Filter
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Yuri A. Abramovich: IUPUI, Department of Mathematics
Wolfgang Filter: ETH-Zentrum, Mathematik

A chapter in Positive Operators and Semigroups on Banach Lattices, 1992, pp 23-26 from Springer

Abstract: Abstract The well-known Ogasawara-Maeda-Vulikh representation theorem asserts that for each Archimedean vector lattice L there exists an extremally disconnected compact Hausdorff space Ω, unique up to a homeomorphism, such that L can be represented isomorphically as an order dense vector sublattice $$\hat L$$ of the universally complete vector lattice C ∞(Ω) of all extended-real-valued continuous functions f on Ω for which {ω ∈ Ω: | f(ω)| = ∞} is nowhere dense. Since the early days of using this representation it has been important to find conditions on L such that $$\hat L$$ consists of bounded functions only. The aim of this short article is to present a simple complete characterization of such vector lattices.

Keywords: representation by bounded functions; Archimedean vector lattice (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-94-017-2721-1_2

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