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arXiv · 1307.8373

On the lattice structure of weakly continuous operators on the space of measures

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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Moritz Gerlach, Markus Kunze. 2013-07-31. On the lattice structure of weakly continuous operators on the space of measures. https://doi.org/10.1002/mana.201300218

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