Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-19T15:46:02.874Z Has data issue: false hasContentIssue false
  • English
  • Français

Génératrices Extrémales d'un Cône de Fonctionnelles Linéaires Positives Invariantes

Published online by Cambridge University Press:  20 November 2018

Jacques Dubois
Jacques Dubois*
Affiliation:
Université de Sherbrooke, Sherbrooke, Québec
Rights & Permissions [Opens in a new window]

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.

Si S est un espace topologique compact séparé et si ϕ : S → S est une fonction continue, l'opérateur: A : C(S) → C(S), défini par Ag = g o ϕ est linéaire positif tel que Ae = e (sur C(S) nous considérons le cône usuel et e désigne la fonction identiquement 1 sur S).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 733 - 747
Copyright
Copyright © Canadian Mathematical Society 1973

References

Bibliographie

1. Bonsall, F. F., Sublinear junctionals and ideals in partially ordered vector spaces, Proc. London Math. Soc. 4 (1954), 402–418.Google Scholar
2. Choquet, G., Lectures on analysis. Vol. II (Benjamin Inc., New York, 1969).Google Scholar
3. Choquet, G. et Deny, J., Sur l'équation de convolution ix = n*<r, C. R. Acad. Sci. Paris Sér. A-B 250 (1960), 799–801.Google Scholar
4. Dubuc, S., Fonctionnelles linéaires positives extrémales, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), 1502–1504.Google Scholar
5. Dunford, N. and Schwartz, J. T., Linear operators. Part I (Wiley (Interscience), New York, 1958).Google Scholar
6. Ellis, A. J., The duality of partially ordered normed linear spaces, J. London Math. Soc. 39 (1964), 730–744.Google Scholar
7. Glicksberg, I., On convex hulls of translates, Pacific J. Math. 13 (1963), 97–113.Google Scholar
8. Halmos, P. R., Lectures on ergodic theory (Publications of the Mathematical Society of Japan, vol. 3, Tokyo, 1956).Google Scholar
9. Kakutani, S., Mean ergodic theorem in abstract (L)-spaces, Proc. Japan Acad. 15 (1939), 121–123.Google Scholar
10. Krein, M. G., and Rutman, M. A., Linear operators leaving invariant a cone in a Banach space, Uspehi Mat. Nauk. 23 (1948), 3–95; Amer. Math. Soc. Transi. 26 (1950).Google Scholar
11. Peressini, A. L., Ordered topological vector spaces (Harper and Row, New York, 1967).Google Scholar
12. Schaefer, H. H., Invariant ideals of positive operators in C(X). I, Illinois J. Math. 11 (1967), 703–715.Google Scholar
13. Schaefer, H. H., Invariant ideals of positive operators in C(X). II, Illinois J. Math. 12 (1968), 525–538.Google Scholar
14. Yosida, K., Functional analysis (Springer-Verlag, Band 123, 1966).Google Scholar