Abstract
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 give applications of these results to Hardy spaces by showing the spacesH p (Tn) are mutually non-isomorphic for differing values ofn when 0<p<1.
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The research of the first two authors was partially supported by NSF-grant DMS 8901636.
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Kalton, N.J., Leranoz, C. & Wojtaszczyk, P. Uniqueness of unconditional bases in quasi-banach spaces with applications to Hardy spaces. Israel J. Math. 72, 299–311 (1990). https://doi.org/10.1007/BF02773786
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DOI: https://doi.org/10.1007/BF02773786