Positivity

, Volume 13, Issue 3, pp 543–558 | Cite as

An Andô-Douglas type theorem in Riesz spaces with a conditional expectation

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Abstract

In this paper we formulate and prove analogues of the Hahn-Jordan decomposition and an Andô-Douglas-Radon-Nikodým theorem in Dedekind complete Riesz spaces with a weak order unit, in the presence of a Riesz space conditional expectation operator. As a consequence we can characterize those subspaces of the Riesz space which are ranges of conditional expectation operators commuting with the given conditional expectation operators and which have a larger range space. This provides the first step towards a formulation of Markov processes on Riesz spaces.

Keywords

Riesz spaces Andô-Douglas theorem Radon-Nikodým theorem Hahn-Jordan decomposition 

Mathematics Subject Classification (2000)

47B60 60G40 60G48 60G42 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.School of MathematicsUniversity of the WitwatersrandWitwatersrandSouth Africa

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