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

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.

preprint2013arXivOpen access
Moritz GerlachMarkus Kunze
math.FA
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Moritz GerlachMarkus Kunze

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