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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Operators on Banach lattices and the Radon-Nikodým theorem


Author: William Feldman
Journal: Proc. Amer. Math. Soc. 100 (1987), 517-521
MSC: Primary 47B55; Secondary 46B30
MathSciNet review: 891156
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Abstract: For positive operators between Banach lattices a concept of absolute continuity is considered. On an AM-space with order unit norm, $ S$ is shown to be absolutely continuous with respect to $ T$ if and only if there is an approximation of $ S$ by finite sums of operators of the type $ q \circ T \circ h$ where $ h$ and $ q$ are multiplication operators or orthomorphisms. Given $ T$ compact, compactness of $ S$ is characterized.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0891156-9
Article copyright: © Copyright 1987 American Mathematical Society