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Continuity and equicontinuity of semigroups on norming dual pairs

Type of Publication: Journal article
Publication status: Published
Author: Kunze, Markus
Year of publication: 2009
Published in: Semigroup Forum ; 79 (2009), 3. - pp. 540-560. - ISSN 0037-1912. - eISSN 1432-2137
DOI (citable link): https://dx.doi.org/10.1007/s00233-009-9174-9
Summary:
We study continuity and equicontinuity of semigroups on norming dual pairs with respect to topologies defined in terms of the duality. In particular, we address the question whether continuity of a semigroup already implies (local/quasi) equicontinuity. We apply our results to transition semigroups and show that, under suitable hypothesis on E, every transition semigroup on Cb(E) which is continuous with respect to the strict topology β 0 is automatically quasi-equicontinuous with respect to that topology. We also give several characterizations of β 0-continuous semigroups on Cb(E) and provide a convenient condition for the transition semigroup of a Banach space valued Markov process to be β 0-continuous.
Subject (DDC): 510 Mathematics
Keywords: Norming dual pairs, Transition semigroups, Equicontinuity, Strict topology

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KUNZE, Markus, 2009. Continuity and equicontinuity of semigroups on norming dual pairs. In: Semigroup Forum. 79(3), pp. 540-560. ISSN 0037-1912. eISSN 1432-2137. Available under: doi: 10.1007/s00233-009-9174-9

@article{Kunze2009-12Conti-41258, title={Continuity and equicontinuity of semigroups on norming dual pairs}, year={2009}, doi={10.1007/s00233-009-9174-9}, number={3}, volume={79}, issn={0037-1912}, journal={Semigroup Forum}, pages={540--560}, author={Kunze, Markus} }

Continuity and equicontinuity of semigroups on norming dual pairs 2018-02-06T14:05:31Z eng 2018-02-06T14:05:31Z Kunze, Markus We study continuity and equicontinuity of semigroups on norming dual pairs with respect to topologies defined in terms of the duality. In particular, we address the question whether continuity of a semigroup already implies (local/quasi) equicontinuity. We apply our results to transition semigroups and show that, under suitable hypothesis on E, every transition semigroup on C<sub>b</sub>(E) which is continuous with respect to the strict topology β <sub>0</sub> is automatically quasi-equicontinuous with respect to that topology. We also give several characterizations of β <sub>0</sub>-continuous semigroups on C<sub>b</sub>(E) and provide a convenient condition for the transition semigroup of a Banach space valued Markov process to be β <sub>0</sub>-continuous. 2009-12 Kunze, Markus

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