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An integral representation of disjointly additive order preserving operators in L1
To konrad jacobs on the occasion of his sixtieth birthday
Authors:
Ulrich Krengel a;
Michael Lin b
| Affiliations: | a Institut f r Mathematische Stochastik, G ttingen, W-Germany |
| b Department of Mathematics and Computer Science, Ben Gurion University of the Negev, Beer Sheva, Israel |
DOI:
10.1080/07362998808809150
Publication Frequency:
6 issues per year
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(English)
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Abstract
We give an integral representation of disjointly additive order preserving nonexpansive operators in L1, using a family
 Pt,t ∈ R of substochastic kernels. We also characterize the case when the kernels correspond to positive linear operators Tt in L1 of norm ≤ 1. For  we then obtain where Xtf is the indicator function of f > t
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| Keywords: Disjointly Additive Operator; Integral Representation; Random Mass Transport; Nonlinear Markov Type Operator |
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