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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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Some Applications of Rademacher Sequences in Banach Lattices

Chen, Z.L.; Wickstead, A.W.
Positivity , Volume 2 (2) – Oct 7, 2004
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References (14)

Publisher
Springer Journals
Copyright
Copyright © 1998 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
DOI
10.1023/A:1009767118180
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Positivity – Springer Journals

Published: Oct 7, 2004

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