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 \(0<p<1\).


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