On the lattice structure of kernel operators |
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| Authors: | Moritz Gerlach Markus Kunze |
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| Abstract: | 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. |
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| Keywords: | Lattice structure transition kernel weak topology Doob's theorem Primary: 47B65 Secondary: 60B10 60J35 |
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