Some Applications of Rademacher Sequences in Banach Lattices

Some Applications of Rademacher Sequences in Banach Lattices 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

Some Applications of Rademacher Sequences in Banach Lattices

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Kluwer Academic Publishers
Copyright © 1998 by Kluwer Academic Publishers
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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