An integral representation of disjointly additive order preserving operators inL1
Ulrich Krengel, Michael Lin · Stochastic Analysis and Applications · 1988
We give an integral representation of disjointly additive order preserving nonexpansive operators in L 1, using a family {Pt ,t ∊ R} of substochastic kernels. We also characterize the case when the kernels correspond to positive linear operators Tt in L 1 of norm ≤ 1. For we then obtain where Xtf is the indicator function of {f > t}