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On nonatomic Banach lattices and Hardy spaces

Nigel J. Kalton·P. Wojtaszczyk
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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 J. Bourgain are used to show that spaces $H_1(\bold T^n)$ are not isomorphic to nonatomic Banach lattices. We also show that tent spaces introduced in \cite{4} are isomorphic to Rad $H_1$.

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Nigel J. Kalton, P. Wojtaszczyk. 1992-06-05. On nonatomic Banach lattices and Hardy spaces. https://arxiv.org/abs/math/9206202

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