J Austral Math Soc Ser A 47 pp90--94, 1989.

Positive Semigroups of Operators on Banach Spaces

K. F. Ng

Abstract

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 ³ a}, where N(A) = sup{N(Aa) | N(a) £ 1} for operator A. A corresponding result on C₀*-semigroups is also given.

1980 AMS Subject Classification (1985 Revision): 47D05, 47H07, 47B44, 46A40

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Authors

K. F. Ng

Department of Mathematics, Chinese University of Hong Kong, Hong Kong.