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Ultra Feller operators from a functional-analytic perspective

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2024

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Dobrick, Alexander
Hölz, Julian

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Studia Mathematica. Institute of Mathematics, Polish Academy of Sciences. 2024, 279(3), S. 243-271. ISSN 0039-3223. eISSN 1730-6337. Verfügbar unter: doi: 10.4064/sm240119-2-8

Zusammenfassung

It is widely known that the product of two positive strong Feller operators on a Polish space E enjoys the ultra Feller property.We present a functional-analytic proof of this fact that allows us to drop the assumption that the operators are positive, and also extends the applicability of this result to more general state spaces. As it turns out, this result can be considered to be a variant of the theorem that on a Banach space with the Dunford–Pettis property, the product of two weakly compact operators is compact.

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Fachgebiet (DDC)
510 Mathematik

Schlagwörter

strong Feller property, ultra Feller property, weak compactness

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ISO 690DOBRICK, Alexander, Julian HÖLZ, Markus KUNZE, 2024. Ultra Feller operators from a functional-analytic perspective. In: Studia Mathematica. Institute of Mathematics, Polish Academy of Sciences. 2024, 279(3), S. 243-271. ISSN 0039-3223. eISSN 1730-6337. Verfügbar unter: doi: 10.4064/sm240119-2-8
BibTex
@article{Dobrick2024Ultra-71475,
  year={2024},
  doi={10.4064/sm240119-2-8},
  title={Ultra Feller operators from a functional-analytic perspective},
  number={3},
  volume={279},
  issn={0039-3223},
  journal={Studia Mathematica},
  pages={243--271},
  author={Dobrick, Alexander and Hölz, Julian and Kunze, Markus}
}
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