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On linear operators on ordered banach spaces

  • Sadayuki Yamamuro (a1)

Abstract

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.

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Copyright

References

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[1]Arendt, Wolfgang, Chernoff, Paul R. and Kato, Tosio, “A generalization of dissipativity and positive semigroups”, J. Operator Theory 8 (1982), 167180.
[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.
[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).
[4]Robinson, Derek W., “Continuous semigroups on ordered Banach spaces” (Mathematics Research Report, 17. Australian National University, Canberra, 1982).
[5]Robinson, Derek W., “On positive semigroups” (Mathematics Research Report, 18. Australian National University, Canberra, 1982).
[6]Robinson, Derek W. and Yamamuro, Sadayuki, “The Jordan decomposition and half-norms”, Pacific J. Math. (to appear).
[7]Robinson, Derek W. and Sadayuki Yamamuro, “Addition of an identity to an ordered Banach space”, J. Austral. Math. Soc. Ser. A (to appear).
[8]Robinson, Derek W. and Sadayuki Yamamuro, “Hereditary cones, order ideals and half-norms”, Pacific J. Math. (to appear).
[9]Robinson, Derek W. and Yamamuro, Sadayuki, “The canonical half-norm, dual half-norms and monotonic norms”, Tohoku Math. J. (to appear).
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On linear operators on ordered banach spaces

  • Sadayuki Yamamuro (a1)

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