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Weak Sequential Compactness and Completeness in Riesz Spaces

Published online by Cambridge University Press:  20 November 2018

Owen Burkinshaw  and
Peter Dodds
Owen Burkinshaw
Affiliation:
Indiana-Purdue University, Indianapolis, Indiana
Peter Dodds
Affiliation:
Flinders University, Bedford Park, Australia
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1332 - 1339
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Burkinshaw, Owen, Weak compactness in the order dual of a vector lattice, Trans. Amer. Math. Soc. 187 (1974), 105–125.Google Scholar
2. Fremlin, D. H., Topological Riesz spaces and measure theory (Cambridge University Press, 1974).Google Scholar
3. Meyer-Nieberg, Peter, Zur schwachen kompactheit in Banachverb linden, Math. Zeit. 134 (1973), 303–315.Google Scholar
4. Hidegorô Nakano, , Modulared semi-ordered linear spaces (Maruzen, Tokyo, 1950).Google Scholar
5. Luxemburg, W. A. J., Notes on Banach function spaces, XIV A Koninkl. Nederl. Akad. Wetensch. Proc. Ser. A68 No. 2 (1965), 230–240.Google Scholar
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, 519–543.Google Scholar
7. Luxemburg, W. A. J. and Zaanen, A. C., Compactness of integral operators in Banach function spaces, Math. Ann. 140 (1963), 150–180.Google Scholar
8. Luxemburg, W. A. J. and Zaanen, A. C., Riesz spaces I (North Holland, 1971).Google Scholar