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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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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DOI: https://doi.org/10.1007/978-1-4419-7515-7_8
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