## Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces.(English)Zbl 0753.46013

Summary: We prove some general results on the uniqueness of unconditional bases in quasi-Banach spaces. We show in particular that certain Lorentz spaces have unique unconditional bases answering a question of Nawrocki and Ortynski. We then given applications of these results to Hardy spaces by showing the spaces $$H_ p({\mathbf T}^ n)$$ are mutually non-isomorphic for differing values of $$n$$ when $$0<p<1$$.

### MSC:

 46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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### References:

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