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Weak Sequential Compactness and Completeness in Riesz Spaces

  • Owen Burkinshaw (a1) and Peter Dodds (a2)

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If L is an Archimedean Riesz space and M an ideal in the order dual of L, the subset A of L is called M-equicontinuous if and only if each monotone decreasing sequence of positive elements of M is uniformly Cauchy on A.

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References

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1. Burkinshaw, Owen, Weak compactness in the order dual of a vector lattice, Trans. Amer. Math. Soc. 187 (1974), 105125.
2. Fremlin, D. H., Topological Riesz spaces and measure theory (Cambridge University Press, 1974).
3. Meyer-Nieberg, Peter, Zur schwachen kompactheit in Banachverb linden, Math. Zeit. 134 (1973), 303315.
4. Hidegorô Nakano, , Modulared semi-ordered linear spaces (Maruzen, Tokyo, 1950).
5. Luxemburg, W. A. J., Notes on Banach function spaces, XIV A Koninkl. Nederl. Akad. Wetensch. Proc. Ser. A68 No. 2 (1965), 230240.
6. Luxemburg, W. A. J. and Zaanen, A. C., Notes on Banach function spaces, VI-XIII, Koninkl. Nederl. Akad. Wetensch. Proc. Ser. A66 (1963), 251-263, 496-504, 655-681; A67 (1964), 104-119, 360-376, 493-581, 519543.
7. Luxemburg, W. A. J. and Zaanen, A. C., Compactness of integral operators in Banach function spaces, Math. Ann. 140 (1963), 150180.
8. Luxemburg, W. A. J. and Zaanen, A. C., Riesz spaces I (North Holland, 1971).
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Weak Sequential Compactness and Completeness in Riesz Spaces

  • Owen Burkinshaw (a1) and Peter Dodds (a2)

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