Estimates of Disjoint Sequences in Banach Lattices and R.I. Function Spaces

Estimates of Disjoint Sequences in Banach Lattices and R.I. Function Spaces We introduce UDS p -property (resp. UDT q -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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Estimates of Disjoint Sequences in Banach Lattices and R.I. Function Spaces

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2005 by Springer
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-003-2714-8
Publisher site
See Article on Publisher Site

Abstract

We introduce UDS p -property (resp. UDT q -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

Journal

PositivitySpringer Journals

Published: Feb 9, 2003

References

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