An integral representation of disjointly additive order preserving operators in l1

Ulrich Krengel; Michael Lin

doi:10.1080/07362998808809150

An integral representation of disjointly additive order preserving operators in l₁

Ulrich Krengel
, Michael Lin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	289-304
Number of pages	16
Journal	Stochastic Analysis and Applications
Volume	6
Issue number	3
DOIs	https://doi.org/10.1080/07362998808809150
State	Published - 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

Access to Document

10.1080/07362998808809150

Cite this

@article{975959405c5f44a5aebda895449d7d25,

title = "An integral representation of disjointly additive order preserving operators in l1",

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\}.",

keywords = "Disjointly additive operator, integral representation, mass transport, nonlinear Markov type operator, random",

author = "Ulrich Krengel and Michael Lin",

year = "1988",

month = jan,

day = "1",

doi = "10.1080/07362998808809150",

language = "English",

volume = "6",

pages = "289--304",

journal = "Stochastic Analysis and Applications",

issn = "0736-2994",

publisher = "Taylor and Francis Ltd.",

number = "3",

}

TY - JOUR

T1 - An integral representation of disjointly additive order preserving operators in l1

AU - Krengel, Ulrich

AU - Lin, Michael

PY - 1988/1/1

Y1 - 1988/1/1

N2 - 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}.

AB - 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}.

KW - Disjointly additive operator

KW - integral representation

KW - mass transport

KW - nonlinear Markov type operator

KW - random

UR - https://www.scopus.com/pages/publications/84931136355

U2 - 10.1080/07362998808809150

DO - 10.1080/07362998808809150

M3 - Article

AN - SCOPUS:84931136355

SN - 0736-2994

VL - 6

SP - 289

EP - 304

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 3

ER -