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A Note on Preserved Smoothness

By Wee-Kee Tang


* Supported by NSERC (Canada)Let X be a Banach space equipped with norm || · ||. We say that || · || is Gâteaux differentiable at x if for every h ∈ SX(|| · ||), (∗) lim t→0 (||x + th|| − ||x||) / t exists. We say that the norm || · || is Gâteaux differentiable if || · || is Gâteaux differentiable at all x ∈ SX(|| · ||)

Topics: Renormings, Gâteaux Differentiability, Octahedral Norms
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Year: 1996
OAI identifier:

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