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Banach Space Theory pp 479–519Cite as

Dentability and Differentiability

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Abstract

The main topic of the present chapter is the dentability of bounded sets and the closely related Radon–Nikodým property (RNP) of Banach spaces. This property has several equivalent characterizations and applications. In particular, Asplund spaces are characterized by the Radon–Nikodým property of their dual spaces. As another application, we show that Lipschitz mappings from separable Banach spaces into Banach spaces with RNP are at some points Gâteaux differentiable.

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Authors and Affiliations

  1. Mathematical Institute of the Academy of Sciences of the Czech Republic, Žitná 25, Praha 1, 11567, Prague, Czech Republic

    Marián Fabian & Petr Hájek

  2. Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 16627, Prague, Czech Republic

    Petr Habala

  3. Departamento de Matematica Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain

    Vicente Montesinos

  4. Department of Mathematical and Statistical Sciences, University of Alberta, Central Academic Building, Edmonton, T6G 2G1, Alberta, Canada

    Václav Zizler

Authors
  1. Marián Fabian
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  2. Petr Habala
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  4. Vicente Montesinos
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  5. Václav Zizler
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Correspondence to Marián Fabian .

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Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V. (2011). Dentability and Differentiability. In: Banach Space Theory. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7515-7_11

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