Journal Article

High Order Smoothness and Roughness in Banach Spaces

R. Gonzalo

in The Quarterly Journal of Mathematics

Volume 50, issue 1, pages 75-86
Published in print March 2000 | ISSN: 0033-5606
Published online March 2000 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmathj/50.1.75
High Order Smoothness and Roughness in Banach Spaces

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We study the existence of equivalent norms nowhere k-times Fréchet differentiable (k ≥ 2) on Banach spaces, introducing the notion of high order roughness. We also study the existence of bump functions with high order Taylor expansions on subsymmetric spaces. Finally we prove that there is no uniformly twice Fréchet differentiable bump function on the 2-convexified Tsirelson space.

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Subjects: Pure Mathematics

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