Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T06:57:05.360Z Has data issue: false hasContentIssue false
  • English
  • Français

On linear operators on ordered banach spaces

Published online by Cambridge University Press:  17 April 2009

Sadayuki Yamamuro
Sadayuki Yamamuro
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, PO Box 4, Canberra, ACT 2600, Australia.
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.

The order structure of the space of all continuous linear operators on an ordered Banach space is studied. The main topic is the Robinson property, that is, the norm of a positive linear operator is attained on the positive unit cone.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 2 , April 1983 , pp. 285 - 305
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Arendt, Wolfgang, Chernoff, Paul R. and Kato, Tosio, “A generalization of dissipativity and positive semigroups”, J. Operator Theory 8 (1982), 167–180.Google Scholar
[2]Grosberg, J. et Krein, M., “Sur la décomposition des fonctionelles en composantes positives”, C.R. (Dokl.) Acad. Sci. URSS (N.S.) 25 (1939), 723–726.Google Scholar
[3]Канторович, Л.В., Вулих, Б.З. и Пинснер, А.Г. [Kantorovitch, L.V., Vulikh, B.Z. and Pinsker, A.G.], Функuuонɑлɒныuŭ ɑнɑлuз є nолууnоря∂оченных nросмрɑлɒнсменх [Functional analysis in partially ordered spaces] (Gos. Izdat. Tehn.-Teor. Lit., Moscow, 1950).Google Scholar
[4]Robinson, Derek W., “Continuous semigroups on ordered Banach spaces” (Mathematics Research Report, 17. Australian National University, Canberra, 1982).Google Scholar
[5]Robinson, Derek W., “On positive semigroups” (Mathematics Research Report, 18. Australian National University, Canberra, 1982).Google Scholar
[6]Robinson, Derek W. and Yamamuro, Sadayuki, “The Jordan decomposition and half-norms”, Pacific J. Math. (to appear).Google Scholar
[7]Robinson, Derek W. and Sadayuki Yamamuro, “Addition of an identity to an ordered Banach space”, J. Austral. Math. Soc. Ser. A (to appear).Google Scholar
[8]Robinson, Derek W. and Sadayuki Yamamuro, “Hereditary cones, order ideals and half-norms”, Pacific J. Math. (to appear).Google Scholar
[9]Robinson, Derek W. and Yamamuro, Sadayuki, “The canonical half-norm, dual half-norms and monotonic norms”, Tohoku Math. J. (to appear).Google Scholar