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Positivity

, Volume 9, Issue 3, pp 369–383 | Cite as

Operators Represented by Conditional Expectations and Random Measures

  • J. J. GroblerEmail author
  • D. T. Rambane
Article

Abstract

On standard measure spaces every order continuous linear map between two ideals of almost everywhere finite measurable functions can be represented by a random measure. An analogue of this theorem is proved for the case of arbitrary σ-finite measure spaces. This fact leads to a proof that every order continuous linear map between ideals of almost everywhere finite measurable functions on σ-finite measure spaces is multiplication conditional expectation representable. This sheds further light on the structure of order continuous operators.

Keywords

random measure multiplication conditional expectation operator pseudo-integral operator order continuous operator 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Unit for Business Mathematics and InformaticsNorth-West UniversityPotchefstroomSouth Africa
  2. 2.Department of Mathematics and Applied MathematicsUniversity of VendaThohoyandouSouth Africa

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