Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T14:09:03.565Z Has data issue: false hasContentIssue false
  • English
  • Français

A maximum principle

Published online by Cambridge University Press:  09 April 2009

Kung-Fu Ng
Kung-Fu Ng
Affiliation:
Mathematics Department Science Centre The Chinese University of Hong Kong Shatin, N. T. Hong Kong
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 K be a nonempty compact set in a Hausdorff locally convex space, and F a nonempty family of upper semicontinuous convex-like functions from K into [–∞, ∞). K is partially ordered by F in a natural manner. It is shown among other things that each isotone, upper semicontinuous and convex-like function g: K → [ – ∞, ∞) attains its K-maximum at some extreme point of K which is also a maximal element of K.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 46 A 40.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1979 , pp. 23 - 26
Copyright
Copyright © Australian Mathematical Society 1979

References

Conway, J. B. (1973), Functions of one complex variable (Graduate texts in mathematics, Springer-Verlag, Berlin).CrossRefGoogle Scholar
Edwards, D. A. (1970), ‘An extension of Choquet boundary theory to certain partially ordered compact convex sets’, Studia Math. 36, 177–193.CrossRefGoogle Scholar
Lumer, G. (1963), ‘Points extrémeaux associés; frontiéres de Shilov et Choquet; principe du minimum’, C. R. Acad. Sc. Paris 256, 858–861.Google Scholar
Wong, Y. C. and Ng, K. F. (1973), Partially ordered topological vector spaces (Clarendon Press, Oxford).Google Scholar
Schaefer, H. H. (1974), Banach lattices and positive operators (Springer-Verlag, Berlin).CrossRefGoogle Scholar