SOME APPLICATIONS OF RADEMACHER SEQUENCES IN BANACH-LATTICES

We give several applications of Rademacher sequences in abstract Banac h lattices. We characterise those Banach lattices with an atomic dual in terms of weak sequential convergence. We give an alternative treat ment of results of Rosenthal, generalising a classical result of Pitt, on the compactness of operators from L-p into L-q. Finally we general ise earlier work of ours by showing that, amongst Banach lattices F wi th an order continuous norm, those having the property that the linear span of the positive compact operators from E into F is complete unde r the regular norm for all Banach lattices E are precisely the atomic lattices. Mathematics Subject Classifications (1991): 46B42, 47B65.