On nonatomic Banach lattices and Hardy spaces

Nigel J. Kalton; P. Wojtaszczyk

On nonatomic Banach lattices and Hardy spaces

Functional Analysis 2008-02-03 v1

Authors: Nigel J. Kalton , P. Wojtaszczyk

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 $H_1$ .

Keywords

banach spaces banach space properties banach algebras

Cite

@article{arxiv.math/9206202,
  title  = {On nonatomic Banach lattices and Hardy spaces},
  author = {Nigel J. Kalton and P. Wojtaszczyk},
  journal= {arXiv preprint arXiv:math/9206202},
  year   = {2008}
}

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