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Smooth Partitions of Unity on Certain C(K) Spaces

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

Published online by Cambridge University Press:  21 December 2009

Petr Hájek
Petr Hájek
Affiliation:
Mathematical Institute, Czech Academy of Science, Žitná 25, Praha, 11567, Czech Rep. E-mail: hajek@math.cas.cz
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Extract

One of the main open problems in the theory of Asplund spaces is whether every Asplund space admits a Fréchet differentiable bump function. This problem is also open for C(K) Asplund spaces, where it is unknown even for C∞-Fréchet smooth bump (a general Asplund space does not always admit C2-Fréchet smooth bump – it suffices to consider ℓ3/2[DGZ2]).

MSC classification

Secondary: 46B03: Isomorphic theory (including renorming) of Banach spaces 46B10: Duality and reflexivity
Type
Research Article
Information
Mathematika , Volume 52 , Issue 1-2 , December 2005 , pp. 131 - 138
Copyright
Copyright © University College London 2005

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References

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