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On linear operators on ordered banach spaces

Published online by Cambridge University Press:  17 April 2009

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

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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
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), 167180.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), 723726.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