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Positive semigroups of operators on Banach spaces

Part of: Nonlinear operators and their properties Special classes of linear operators Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

K. F. Ng
K. F. Ng
Affiliation:
Department of Mathematics, Chinese University of Hong Kong, Hong Kong
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Abstract

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We prove a version of the Feller-Miyadera-Phillips theorem characterizing the infinitesimal generators of positive C0-semigroups on ordered Banach spaces with normal cones. This is done in terms of N(A) as well as the canonical half-norms of Arendt Chernoff and Kato defined by N(a) = inf{‖b‖ |b ≥ a}, where N(A) = sup{N(Aa) |N(a) ≶ 1} for operator A. A corresponding result on –semigroups is also given.

MSC classification

Secondary: 47H07: Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces 47B44: Accretive operators, dissipative operators, etc. 46A40: Ordered topological linear spaces, vector lattices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 1 , August 1989 , pp. 90 - 94
Copyright
Copyright © Australian Mathematical Society 1989

References

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