Abstract
For positive operators between Banach lattices a concept of absolute continuity is considered. On an AM-space with order unit norm, S S is shown to be absolutely continuous with respect to T T if and only if there is an approximation of S S by finite sums of operators of the type q ∘ T ∘ h q \circ T \circ h where h h and q q are multiplication operators or orthomorphisms. Given T T compact, compactness of S S is characterized.
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