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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Smooth norms on certain $C(K)$ spaces


Author: Petr Hájek
Journal: Proc. Amer. Math. Soc. 131 (2003), 2049-2051
MSC (2000): Primary 46B03, 46B10, 46B20
Published electronically: February 5, 2003
MathSciNet review: 1963749
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Abstract | References | Similar Articles | Additional Information

Abstract: $C(K)$ spaces admit an equivalent $C^\infty$-smooth renorming whenever $K^{(\omega_1)}=\emptyset$.


References [Enhancements On Off] (What's this?)

  • [D] R. Deville, Problemes de renormages, J. Funct. Anal. 68 (1986), 117-129. MR 87m:46035
  • [DGZ] R. Deville, G. Godefroy and V. Zizler, Smoothness and renormings in Banach spaces (1993), Longman. MR 94d:46012
  • [Di] J. Dieudonné, Foundations of Modern Analysis (1969), Acad. Press. MR 50:1782
  • [GPWZ] G. Godefroy, J. Pelant, J. H. M. Whitfield and V. Zizler, Banach space properties of Cisielski-Pol's $C(K)$, Proc. AMS 103 (1988), 1087-1094. MR 89i:46042
  • [H] R. Haydon, Trees in renorming theory, Proc. London Math. Soc. 78 (1999), 549-584. MR 2000d:46011

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Additional Information

Petr Hájek
Affiliation: Mathematical Institute, Czech Academy of Science, Žitná 25, Praha, 11567, Czech Republic
Email: hajek@math.cas.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06819-9
PII: S 0002-9939(03)06819-9
Received by editor(s): March 20, 2001
Published electronically: February 5, 2003
Additional Notes: The author was supported by grants AV 1019003, A1 019 205 and GAČR 201/01/11098
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2003 American Mathematical Society