An integral representation of disjointly additive order preserving operators in l1

Ulrich Krengel, Michael Lin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We give an integral representation of disjointly additive order preserving nonexpansive operators in L1, using a family {Pt,t ∊IR} of substochastic kernels. We also characterize the case when the kernels correspond to positive linear operators Ttin L1of norm < 1. For f G∊ L1+we then obtain Tf= ∫0∞ (Xtf)dt where Xtf is the indicator function of {f > t}.

Original languageEnglish
Pages (from-to)289-304
Number of pages16
JournalStochastic Analysis and Applications
Volume6
Issue number3
DOIs
StatePublished - 1 Jan 1988

Keywords

  • Disjointly additive operator
  • integral representation
  • mass transport
  • nonlinear Markov type operator
  • random

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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