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Continuity and equicontinuity of semigroups on norming dual pairs

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2009

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https://doi.org/10.1007/s00233-009-9174-9
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Semigroup Forum. 2009, 79(3), pp. 540-560. ISSN 0037-1912. eISSN 1432-2137. Available under: doi: 10.1007/s00233-009-9174-9

Zusammenfassung

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.

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Fachgebiet (DDC)
510 Mathematik

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Norming dual pairs, Transition semigroups, Equicontinuity, Strict topology

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ISO 690KUNZE, Markus, 2009. Continuity and equicontinuity of semigroups on norming dual pairs. In: Semigroup Forum. 2009, 79(3), pp. 540-560. ISSN 0037-1912. eISSN 1432-2137. Available under: doi: 10.1007/s00233-009-9174-9
BibTex
@article{Kunze2009-12Conti-41258,
  year={2009},
  doi={10.1007/s00233-009-9174-9},
  title={Continuity and equicontinuity of semigroups on norming dual pairs},
  number={3},
  volume={79},
  issn={0037-1912},
  journal={Semigroup Forum},
  pages={540--560},
  author={Kunze, Markus}
}
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