Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T11:54:50.243Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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 spaces46B10: Duality and reflexivity

Information

Type
Research Article
Information
Mathematika , Volume 52 , Issue 1-2 , December 2005, pp. 131 - 138
Copyright
Copyright © University College London 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[D]Deville, R., Problemes de renormages, J. Funct. Anal. 68 (1986), 117–129.Google Scholar
[DGZ1]Deville, R., Godefroy, G. and Zizler, V., The three space problem for smooth partitions of unity and C(K) spaces, Math. Anal. 288 (1990), 613–625.CrossRefGoogle Scholar
[DGZ2]Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces Longman (1993).Google Scholar
[DPWZ]Godefroy, G., Pelant, J., Whitefield, J.H.M. and Zizler, V., Banach space properties of Ciesielski-Pol's C(K), Proc. Amer. Math. Soc. 103 (1988), 1087–1094.Google Scholar
[H1]Haydon, R., Smooth functions and partitions of unity on certain Banach spaces, Quart. J. Math. Oxford 47 (1996), 455–468.Google Scholar
[H2]Haydon, R., Trees in renorming theory, Proc. London Math. Soc. 78 (1999), 549–584.CrossRefGoogle Scholar
[T]Torunczyk, H., Smooth partitions of unity on some nonseparable spaces, Studia Math. 46 (1973), 43–51.CrossRefGoogle Scholar