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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On nonatomic Banach lattices and Hardy spaces


Authors: N. J. Kalton and P. Wojtaszczyk
Journal: Proc. Amer. Math. Soc. 120 (1994), 731-741
MSC: Primary 46B42; Secondary 42B30, 46E15
MathSciNet review: 1181168
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Abstract: We are interested in the question when a Banach space $ X$ with an unconditional basis is isomorphic (as a Banach space) to an order-continuous nonatomic Banach lattice. We show that this is the case if and only if $ X$ is isomorphic as a Banach space with $ X({\ell _2})$. This and results of Bourgain are used to show that spaces $ {H_1}({{\mathbf{T}}^n})$ are not isomorphic to nonatomic Banach lattices. We also show that tent spaces introduced by Coifman, Meyer, and Stein are isomorphic to $ \operatorname{Rad} \;{H_1}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1181168-6
PII: S 0002-9939(1994)1181168-6
Keywords: Order-continuous Banach lattice, Hardy spaces
Article copyright: © Copyright 1994 American Mathematical Society