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.
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References
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© 1992 Springer Science+Business Media Dordrecht
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Abramovich, Y.A., Filter, W. (1992). A Remark on the Representation of Vector Lattices as Spaces of Continuous Real-Valued Functions. In: Huijsmans, C.B., Luxemburg, W.A.J. (eds) Positive Operators and Semigroups on Banach Lattices. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2721-1_2
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DOI: https://doi.org/10.1007/978-94-017-2721-1_2
Publisher Name: Springer, Dordrecht
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