Lattice Properties of Operators Defined By Random Measures

Original Articles

Lattice Properties of Operators Defined By Random Measures

Published in: Quaestiones Mathematicae
Volume 26 , issue 3 , 2003 , pages: 307–319
DOI: 10.2989/16073600309486061
Author(s): J.J. Grobler , B. de Pagter , D.T. Rambane
Keywords: RIESZ SPACE , RANDOM MEASURE , PSEUDO-INTEGRAL OPERATOR , ORDER BOUNDED OPERATOR , ORDER CONTINUOUS OPERATOR
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Abstract

We prove that the lattice properties of operators defined by random measures hold under general conditions on the measure space. This solves a problem found in a paper of A.R. Sourour on these operators and generalizes his results.
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