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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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Article copyright: © Copyright 1987 American Mathematical Society

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