Abstract
We show that the Lipschitz structure of a separable quasi-Banach space does not determine, in general, its linear structure. Using the notion of the Arens-Eells p-space over a metric space for 0 < p ≤ 1 we construct examples of separable quasi-Banach spaces which are Lipschitz isomorphic but not linearly isomorphic.
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The first author was supported by NSF grant DMS-0555670.
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Albiac, F., Kalton, N.J. Lipschitz structure of quasi-Banach spaces. Isr. J. Math. 170, 317–335 (2009). https://doi.org/10.1007/s11856-009-0031-z
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DOI: https://doi.org/10.1007/s11856-009-0031-z