No CrossRef data available.
Article contents
M-spaces with quasi-interior points
Published online by Cambridge University Press: 18 May 2009
Extract
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.
In this paper we characterize those locally convex lattices which can be represented as dense sublatices containing 1 in a space C(X) and whose topologies can be recognized as topologies of uniform convergence on selections of compact subsets of X. Here C(X) is the lattice of continuous real-valued functions on a completely regular space X. The class of such locally convex lattices includes the classical order unit spaces investigated by Kakutani [3], arbitrary products of order unit spaces, for example ∏ L∞ and the order partition spaces studied in [1].
- Type
- Research Article
- Information
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 1982
References
REFERENCES
1.Feldman, W. and Porter, J., “A vector lattice topology and function space representation,” Trans. Amer. Math. Soc. 235 (1978), 193–204.CrossRefGoogle Scholar
2.Jameson, G., Ordered Linear Spaces, Lecture Notes in Mathematics No. 141, (Springer-Verlag, 1970).CrossRefGoogle Scholar
3.Kakutani, S., “Concrete representation of abstract (M)-spaces,” Ann. of Math. (2) 42 (1941), 994–1028.CrossRefGoogle Scholar
4.Kuller, R., “Locally convex topological vector lattices and their representations,” Michigan Math, J. 5 (1958), 83–90.CrossRefGoogle Scholar
5.Michael, E., “Locally multiplicatively-convex topological algebras,” Mem. Amer. Math. Soc., 11 (1952).Google Scholar
6.Schaefer, H., Banach Lattices of Positive Operators. (Springer-Verlag, 1974).CrossRefGoogle Scholar
You have
Access