We give several applications of Rademacher sequences in abstract Banach lattices. We characterise those Banach lattices with an atomic dual in terms of weak* sequential convergence. We give an alternative treatment of results of Rosenthal, generalising a classical result of Pitt, on the compactness of operators from Lp into Lq. Finally we generalise earlier work of ours by showing that, amongst Banach lattices F with an order continuous norm, those having the property that the linear span of the positive compact operators fromE into F is complete under the regular norm for all Banach lattices E are precisely the atomic lattices.
Positivity – Springer Journals
Published: Oct 7, 2004
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