On the lattice structure of kernel operators
| Type of Publication: | Journal article |
| Publication status: | Published |
| Author: | Gerlach, Moritz; Kunze, Markus |
| Year of publication: | 2015 |
| Published in: | Mathematische Nachrichten ; 288 (2015), 5-6. - pp. 584-592. - ISSN 0025-584X. - eISSN 1522-2616 |
| ArXiv-ID: | arXiv:1307.8373 |
| DOI (citable link): | https://dx.doi.org/10.1002/mana.201300218 |
| Summary: |
Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a sublattice that is lattice isomorphic to the space of transition kernels. As an application we present a purely analytic proof of Doob's theorem concerning stability of transition semigroups.
|
| Subject (DDC): | 510 Mathematics |
| Keywords: | Lattice structure, transition kernel, weak topology, Doob’s theorem |
| Bibliography of Konstanz: | Yes |
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GERLACH, Moritz, Markus KUNZE, 2015. On the lattice structure of kernel operators. In: Mathematische Nachrichten. 288(5-6), pp. 584-592. ISSN 0025-584X. eISSN 1522-2616. Available under: doi: 10.1002/mana.201300218
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