Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T02:19:09.307Z Has data issue: false hasContentIssue false

A cone characterisation of reflexive locally convex spaces

Published online by Cambridge University Press:  17 April 2009

Jinghui Qiu
Affiliation:
Department of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, People's Republic of China
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.

In this paper, we find the dual relationship between solidness and the angle property of cones, which is characteristic of reflexivity for locally convex spaces.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Cesari, L. and Suryanarayana, M.B., ‘Existence theorems for Pareto optimisation: multivalued and Banach space valued functionals’, Trans. Amer. Math. Soc. 244 (1978), 3765.CrossRefGoogle Scholar
[2]Han, Z.Q., ‘Remarks on the angle property and solid cones’, J. Optim. Theory Appl. 82 (1994), 149157.CrossRefGoogle Scholar
[3]Han, Z.Q., ‘Relations between solid cones and cones satisfying angle property’, J. Systems Sci. Math. Sci. 18 (1998), 1822.Google Scholar
[4]Jameson, G., Ordered linear spaces (Springer-Verlag, Berlin Heidelberg, New York, 1970).CrossRefGoogle Scholar
[5]Köthe, G.Topological vector spaces. I (Springer-Verlag, Berlin, Heidelberg, New York, 1983).CrossRefGoogle Scholar
[6]Qiu, J.H., ‘On solidness of polar cones’ (to appear).Google Scholar
[7]Schaefer, H.H., Topological vector spaces (Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[8]Sterna-Karwat, A., ‘Remarks on convex cones’, J. Optim. Theory Appl. 59 (1988), 335340.CrossRefGoogle Scholar
[9]Wilansky, A., Modern methods in topological vector spaces (McGraw-Hill, New York, 1978).Google Scholar