# On the lattice structure of kernel operators

#### Autoren: Moritz Gerlach, Markus Kunze (2015)

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.

Zeitschrift:
Mathematische Nachrichten
Seiten:
584-592
Band:
288

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