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A short proof for the stability theorem for positive semigroups on 
Author(s):
Lutz
Weis
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3253-3256.
MSC (1991):
Primary 47D06
MathSciNet review:
1469440
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Abstract:
We give a short proof showing that the growth bound of a positive semigroup on  equals the spectral bound of its generator. It is based on a new boundedness theorem for positive convolution operators on  . We also give a counterexample, showing that Gearhart's result does not extend from Hilbert spaces to  -spaces.
References:
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- J. Bergh and J. Löfström, Interpolation Spaces, Springer Verlag, 1976. MR 58:2349
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- R. Nagel (ed.), One Parameter Semigroups of Positive Operators, Springer Verlag, 1986. MR 88i:47022
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- J. van Neerven, The Asymptotic Behavior of a Semigroup of Linear Operators, Birkhäuser Verlag, Basel, Boston, Berlin, 1996. MR 98d:47001
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 spaces, Proc. Amer. Math. Soc. 123 (1995), 3089-3094. MR 95m:47074
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Additional Information:
Lutz
Weis
Affiliation:
Universität Karlsruhe, Mathematisches Institut I, Postfach 69 80, Englerstrasse 2, 76128 Karlsruhe, Germany
Email:
Lutz.Weis@math.uni-Karlsruhe.de
DOI:
10.1090/S0002-9939-98-04612-7
PII:
S 0002-9939(98)04612-7
Keywords:
Stability of semigroups,
positive operators
Received by editor(s):
July 22, 1996
Received by editor(s) in revised form:
March 12, 1997
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
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