On nonatomic Banach lattices and Hardy spaces
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- by N. J. Kalton and P. Wojtaszczyk PDF
- Proc. Amer. Math. Soc. 120 (1994), 731-741 Request permission
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 $\operatorname {Rad} \;{H_1}$.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 731-741
- MSC: Primary 46B42; Secondary 42B30, 46E15
- DOI: https://doi.org/10.1090/S0002-9939-1994-1181168-6
- MathSciNet review: 1181168