Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-16T10:32:22.862Z Has data issue: false hasContentIssue false
  • English
  • Français

Positive semigroups of operators on Banach spaces

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

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
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.

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

[1]Arendt, W., Chernoff, P. R., and Kato, T., ‘A generalization of dissipativity and positive semigroups’, J. Operator Theory 8 (1982), 167–180.Google Scholar
[2]Batty, C. J. K. and Robinson, D. W., ‘Positive one-parameter semigroups on ordered Banach spaces’, Acta Appl. Math. 1 (1984), 221–296.CrossRefGoogle Scholar
[3]Bratteli, O., Digernes, T. and Robinson, D. W., ‘Positive semigroups on ordered Banach spaces’, J. Operator Theory 9 (1983), 371–400.Google Scholar
[4]Davies, E. B., One-parameter semigroups, (Academic Press, London, 1980).Google Scholar
[5]Ng, K. F., ‘The duality of partially ordered Banach spaces’, Proc. London Math. Soc. 19 (1969), 269–288.CrossRefGoogle Scholar
[6]Robinson, D. W. and Yamamuro, S., ‘The Jordan decomposition and half-norms’, Pacific J. Math. 110 (1984), 345–353.CrossRefGoogle Scholar
[7]Robinson, D. W. and Yamamuro, S., ‘The canonical half-norm, dual half-norms and monotonic norms’, Tōhoku Math. J. 35 (1983), 375–386.Google Scholar
[8]Robinson, D. W., ‘Continuous semigroups on ordered Banach Spaces’, J. Funct. Anal. 51 (1983), 268–284.CrossRefGoogle Scholar
[9]Robinson, D. W., ‘On positive semigroups’, Publ. RIMS Kyoto University 20 (1984), 213–224.CrossRefGoogle Scholar