Some Applications of Rademacher Sequences in Banach Lattices
Tóm tắt
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.
Tài liệu tham khảo
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