Geodesic
Norm continuity of $c_0$-semigroups
Studia Mathematica, Tome 134 (1999) no. 2, pp. 169-178

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that a positive semigroup $T_t$ on $L_p(Ω,ν)$ 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 $L_p$-scale, which may be of independent interest.
DOI : 10.4064/sm-134-2-169-178

V. Goersmeyer 1 ; L. Weis 1

1 
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V. Goersmeyer; L. Weis. Norm continuity of $c_0$-semigroups. Studia Mathematica, Tome 134 (1999) no. 2, pp. 169-178. doi: 10.4064/sm-134-2-169-178

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