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Smooth norms on certain spaces

Author(s): Petr Hájek
Journal: Proc. Amer. Math. Soc. 131 (2003), 2049-2051.
MSC (2000): Primary 46B03, 46B10, 46B20
Posted: February 5, 2003
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Abstract: spaces admit an equivalent $C^\infty$ -smooth renorming whenever $K^{(\omega_1)}=\emptyset$ .

References:

[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 , 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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