On the lattice structure of weakly continuous operators on the space of measures
Functional Analysis
2015-11-05 v1
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.
Keywords
Cite
@article{arxiv.1307.8373,
title = {On the lattice structure of weakly continuous operators on the space of measures},
author = {Moritz Gerlach and Markus Kunze},
journal= {arXiv preprint arXiv:1307.8373},
year = {2015}
}
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9 pages, 0 figures