Norm continuity of c0-semigroups
Goersmeyer, V. ; Weis, L.
Studia Mathematica, Tome 133 (1999), p. 169-178 / Harvested from The Polish Digital Mathematics Library
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We show that a positive semigroup Tt on Lp(Ω,ν) with generator A and ||R(α + i β)|| → 0 as |β| → ∞ for some α ∈ ℝ is continuous in the operator norm for t>0. The proof is based on a criterion for norm continuity in terms of “smoothing properties” of certain convolution operators on general Banach spaces and an extrapolation result for the Lp-scale, which may be of independent interest.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:216630 
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     title = {Norm continuity of $c\_0$-semigroups},
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     volume = {133},
     year = {1999},
     pages = {169-178},
     zbl = {0940.47033},
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Goersmeyer, V.; Weis, L. Norm continuity of $c_0$-semigroups. Studia Mathematica, Tome 133 (1999) pp. 169-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv134i2p169bwm/

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