Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-28T14:02:47.840Z Has data issue: false hasContentIssue false
  • English
  • Français

On Levi-Like Properties and some of Their Applications in Riesz Space Theory

Published online by Cambridge University Press:  20 November 2018

G. Buskes  and
I. Labuda
G. Buskes
Affiliation:
Rljksuniversiteit Mathematisch Instituut Budapestlaan6, 3508 TA Utrecht, The Netherlands
I. Labuda
Affiliation:
Department of Mathematics, University of MississippiOxford, Mississippi 38677, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let (L, λ) be a locally solid Riesz space. (L, λ) is said to have the Levi property if for every increasing λ-bounded net (xα) ⊂ L+, sup xα exists. The Levi property, appearing in literature also as weak Fatou property (Luxemburg and Zaanen), condition (B) or monotone completeness (Russian terminology), is a classical object of investigation. In this paper we are interested in some variations of the property, their mutual relationships and applications in the theory of topological Riesz spaces. In the first part of the paper we clarify the status of two problems of Aliprantis and Burkinshaw. In the second part we study ideal-injective Riesz spaces.

Keywords

46A1006F20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 477 - 486
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Abramovich, Y., Some theorems on normed lattices Vestnik Leningrad. Univ. Math. 13 (1971), pp. 5–11.Google Scholar
2. Aliprantis, C. D. and Burkinshaw, O., Locally solid Riesz spaces Academic Press, New York-San Francisco-London, 1978.Google Scholar
3. Buskes, G., Extension of Riesz homomorphisms Thesis 1983, Nijmegen.Google Scholar
4. Buskes, G., Extension of Riesz homomorphisms I Journal of the Austral. Math. Soc. Sci. A, Volume 39 (1985), pp. 107–120.Google Scholar
5. Fremlin, D. H., Topological Riesz spaces and measure theory Cambridge Univ. Press, London-New York, 1974.Google Scholar
6. Fremlin, D. H., Inextensible Riesz spaces Math. Proc. Cambridge Philos. Soc. 77 (1975), pp. 71–89.Google Scholar
7. Fremlin, D. H. Groenewegen, Gé, On spaces of Banach lattice valued functions and measures Thesis 1982, Nijmegen.Google Scholar
8. Labuda, I., On the largest o-enlargement of a locally solid Riesz space Bull. Pol. Acad. Math. 33 (1985), pp. 615–622.Google Scholar
9. Labuda, I., Submeasures and locally solid topologies on Riesz spaces Math. Z., 195 (1987), pp. 179–196.Google Scholar
10. Peressini, A. L., Ordered topological vector spaces Harper & Row, New York, 1967.Google Scholar
11. Semadeni, Z., Banach spaces of continuous functions P.W.N., Warsaw 1971.Google Scholar
12. Veksler, A.I. and Geiler, V. A., Order and disjoint completeness of linear partially ordered spaces Siberian Math. J. 13 (1972), pp. 30–35.Google Scholar