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Smooth functions onc 0

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Abstract

We show that every Fréchet differentiable real function onc 0 with locally uniformly continuous derivative has locally compact derivative. Among the corollaries we obtain that there exists no surjectiveC 2 smooth operator fromc 0 onto an infinite dimensional space with nontrivial type.

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Author notes

  1. Petr Hájek

    Present address: Departemento de Analysis, Universidad Complutense de Madrid, Madrid, Spain

Authors and Affiliations

  1. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada

    Petr Hájek

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  1. Petr Hájek
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Correspondence to Petr Hájek.

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Hájek, P. Smooth functions onc 0 . Isr. J. Math. 104, 17–27 (1998). https://doi.org/10.1007/BF02897057

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  • DOI: https://doi.org/10.1007/BF02897057

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