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C 1-Smoothness in Separable Spaces

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Banach Space Theory

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Abstract

In this chapter we study separable Asplund spaces, i.e., Banach spaces with a separable dual space. These spaces admit many equivalent characterizations, in particular by means of C 1-smooth renormings and differentiability properties of convex functions. Asplund spaces also play an important role in applications. We study basic results in smooth approximation and ranges of smooth nonlinear operators.

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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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  3. Petr Hájek
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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). C 1-Smoothness in Separable Spaces. In: Banach Space Theory. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7515-7_8

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