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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability and dichotomy
of positive semigroups on $L_p$


Author: Stephen Montgomery-Smith
Journal: Proc. Amer. Math. Soc. 124 (1996), 2433-2437
MSC (1991): Primary 47-02, 47D06; Secondary 35B40
MathSciNet review: 1327030
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Abstract | References | Similar Articles | Additional Information

Abstract: A new proof of a result of Lutz Weis is given, that states that the stability of a positive strongly continuous semigroup $(e^{tA})_{t \ge 0}$ on $L_p$may be determined by the quantity $s(A)$. We also give an example to show that the dichotomy of the semigroup may not always be determined by the spectrum $\sigma (A)$.


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Additional Information

Stephen Montgomery-Smith
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: stephen@math.missouri.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03356-4
PII: S 0002-9939(96)03356-4
Received by editor(s): June 14, 1994
Received by editor(s) in revised form: February 17, 1995
Additional Notes: Research supported in part by N.S.F. Grant D.M.S. 9201357.
Communicated by: Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society