Diagonals of positive semigroups |
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Authors: | Ben de Pagter Anton R Schep |
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Institution: | (1) Department of Mathematics, Delft University of Technology, P.O. Box 356, 2600 AJ Delft, The Netherlands;(2) Department of Mathematics, University of South Carolina, 29208 Columbia, SC, USA |
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Abstract: | LetE be a Dedekind complete complex Banach lattice and letD denote the diagonal projection from the spaceL
r
(E) onto the centerZ(E) ofE. Let {T(t)}
t 0 be a positive strongly continuous semigroup of linear operators with generatorA. The first main result is that if the spectral bounds(A) equals to zero, then the functionD(T(t)) is a center valuedp-function. The second main result is that if for >0 the diagonalD(R( , A)) of the resolvent operatorR( , A) is strictly positive, then (D(R( , A)))
–1 is a center valued Bernstein function. As an application of these results it follows that the order limit lim![gamma](/content/m255w066l3205976/xxlarge947.gif) 0 D(R( ,A)) exists inZ(E) and equals the order limit lim
m![rarr](/content/m255w066l3205976/xxlarge8594.gif)
D(( R( , A))
m
) for any >0. |
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Keywords: | 47B65 47D03 47D06 |
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