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The tensor product of Archimedean ordered vector spaces. (English) Zbl 0663.46006
The paper contains remarkable simplifications of the tensor product construction of Archimedean Riesz spaces given previously by D. H. Fremlin [Math. Ann. 211, 87-106 (1974; Zbl 0272.46050)] or H. H. Schaefer [MAA Studies Math. 21, 158-221 (1980; Zbl 0494.46021)]. The authors present two different approaches. The first is analogous to the formation of a free lattice generated by a given partially ordered set. In the second approach it is assumed first that given spaces have the principal projection property and a construction by step-elements is used; arbitrary spaces are embedded into their Dedekind completions. The results are useful in the theory of Banach lattices and give the basic constructions in the theory of Riesz spaces.
Reviewer: B.Riecan

46A40 Ordered topological linear spaces, vector lattices
46M05 Tensor products in functional analysis
46B42 Banach lattices
Full Text: DOI
[1] Fremlin, Mathematika 26 pp 302– (1974)
[2] DOI: 10.1007/BF01344164 · Zbl 0272.46050 · doi:10.1007/BF01344164
[3] DOI: 10.2307/2373758 · Zbl 0252.46094 · doi:10.2307/2373758
[4] DOI: 10.2307/2045027 · Zbl 0541.47032 · doi:10.2307/2045027
[5] Zaanen, Riesz Spaces II (1983)
[6] Wong, Partially Ordered Topological Vector Spaces (1973) · Zbl 0269.46007
[7] Gr?tzer, Lattice Theory, First Concepts and Distributive Lattices (1971)
[8] Schaefer, Banach Lattices and Positive Operators (1974) · Zbl 0296.47023 · doi:10.1007/978-3-642-65970-6
[9] Schaefer, Studies in Functional Analysis pp 158– (1980)
[10] Meyer, C.R. Acad. Sci. Paris S?r. I Math. 283 pp 249– (1976)
[11] Luxemburg, Riesz Spaces I (1971)
[12] Luxemberg, Indag. Math. 41 pp 145– (1979) · doi:10.1016/S1385-7258(79)80009-8
[13] Vulikh, Introduction to the Theory of Partially Ordered Spaces (1967) · Zbl 0186.44601
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