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Some Characterizations of The Projection Property in Archimedean Riesz Spaces

Published online by Cambridge University Press:  20 November 2018

K. K. Kutty  and
J. Quinn
K. K. Kutty
Affiliation:
Queen's University, Kingston, Ontario
J. Quinn
Affiliation:
Loyola University, New Orleans, Louisiana
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In this paper we give some new characterizations of the projection property in Archimedean Riesz spaces. Our approach primarily explores the interrelationships between such things as the band structure or the prime ideal structure of an Archimedean vector lattice and corresponding structures of its Dedekind completion. Our results show that, in general, there is a ‘strong“ relationship if and only if the original vector lattice has the projection property. The main result of this paper is Theorem 2.6 which both summarizes and extends all of the results we obtain prior to it.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 2 , April 1972 , pp. 306 - 311
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Bourbaki, N., Integration, Chapters I-IV (Hermann, Paris, 1952).Google Scholar
2. Johnson, D. G. and Kist, J. E., Prime ideals in vector lattices, Can. J. Math. 14 (1962), 517–528.Google Scholar
3. Kumaran Kutty, K., Prime ideals in a vector lattice and its Dedekind Completion, Ph.D. Thesis, Michigan State University, 1970.Google Scholar
4. Luxemburg, W. A. J. and Zaanen, A. C., Riesz spaces, Part I (Preprint of Book).Google Scholar
5. Luxemburg, W. A. J. and Zaanen, A. C., Notes on Banach function spaces, Proc. Acad. Sci. Amsterdam, Note IX, A67, (1964), 360-376.Google Scholar
6. Masterson, J. J., Structure spaces of a vector lattice and its Dedekind completion, Nederl. Acad. Wetensch. Indag. Math. 80 (1968), 486–478.Google Scholar
7. Nakano, H., Modern spectral theory (Maruzen, Tokyo, 1950).Google Scholar