Estimates of disjoint sequences in Banach lattices and R.I. function spaces

Details Estimates of disjoint sequences in Banach lattices and R.I. function spaces Estimates of disjoint sequences in Banach lattices and R.I. function spaces

2004-04-29

arxiv.org/abs/math/0404526v1

Mathematics

Functional Analysis

Scientific paper

We introduce UDSp-property (resp. UDTq-property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to the high order smoothness of Banach lattices, in the sense of the existence of differentiable bump functions.

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