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On C2-smooth norms on c0

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

Petr Hájek
Petr Hájek
Affiliation:
Department of Mathematics, University of Alberta, Edmonton T6G 2G1, Canada.
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Abstract

We show that if the derivative of a convex function on c0 is locally uniformly continuous, then every point x ∈ c0, has a neighbourhood O such that f′(O) is relatively compact in ℓ1.

MSC classification

Secondary: 46B25: Classical Banach spaces in the general theory

Information

Type
Research Article
Information
Mathematika , Volume 43 , Issue 2 , December 1996 , pp. 362 - 370
Copyright
Copyright © University College London 1996

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References

1.Aron, R. M.. Compact polynomials and compact differentiable mappings between Banach spaces. Sèm. Pierre Lelong, Lecture Notes 524, (Springer-Verlag, 1976), 213–222.Google Scholar
2.Deville, R.Fonf, V. and Hájek, P.. Polyhedral and analytic renormings of separable Banach spaces. To appear in Israel J. Math.Google Scholar
3.Hájek, P.. On convex functions in c0(ω1). To appear in Collectanea Math.Google Scholar
4.Hájek, P.. Analytic approximations of symmetric norms in c0. Preprint.Google Scholar
5.Hájek, P.. Smooth norms that depend locally on finitely many coordinates. To appear in Proc. Amer. Math. Soc.Google Scholar