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On Lipschitz Maps, Martingales, and the Radon–Nikodým Property for \({\mathsf{F}}\)-Spaces

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Abstract

The development of the Radon–Nikodým property in Banach spaces sprang from the study of the differentiability of Lipschitz maps from the real line into a space X. Even though there was no initial reason to restrict attention to the locally convex case, the absence of genuine convexity set p-Banach spaces apart and the theory evolved without them. Kalton restored the dignity to quasi-Banach spaces and in 1979 he initiated the search for an analogue of the Radon–Nikodým property for these spaces. Continuing in this spirit, we investigate in this setting the connection between differentiability of Lipschitz maps, limits of martingales, and spaces of bounded operators defined on L p for p < 1.

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Authors and Affiliations

  1. Mathematics Department, Universidad Pública de Navarra, 31006, Pamplona, Spain

    F. Albiac

  2. Department of Mathematics and Computer Sciences, Universidad de La Rioja, 26004, Logroño, Spain

    J. L. Ansorena

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  1. F. Albiac
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  2. J. L. Ansorena
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Correspondence to F. Albiac.

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Albiac, F., Ansorena, J.L. On Lipschitz Maps, Martingales, and the Radon–Nikodým Property for \({\mathsf{F}}\)-Spaces. Mediterr. J. Math. 13, 1963–1980 (2016). https://doi.org/10.1007/s00009-015-0625-0

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  • DOI: https://doi.org/10.1007/s00009-015-0625-0

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