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Title: A note on lattice renormings (English)
Author: Fabian, Marián
Author: Hájek, Petr
Author: Zizler, Václav
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 38
Issue: 2
Year: 1997
Pages: 263-272
Category: math
Summary: It is shown that every strongly lattice norm on $c_0(\Gamma)$ can be approximated by $C^\infty$ smooth norms. We also show that there is no lattice and G\^ateaux differentiable norm on $C_0[0,\omega_1]$. (English)
Keyword: smooth norms
Keyword: approximation
Keyword: lattice norms
Keyword: $c_0(\Gamma)$
Keyword: $C_0[0, \omega_1]$
MSC: 46B03
MSC: 46B20
MSC: 46B26
idZBL: Zbl 0886.46006
idMR: MR1455493
Date available: 2009-01-08T18:30:42Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Deville R., Fonf V., Hájek P.: Analytic and polyhedral approximations of convex bodies in separable polyhedral Banach spaces.Israel J. Math., to appear. MR 1639743
Reference: [2] Deville R., Fonf V., Hájek P.: Analytic and $C^k$-smooth approximations of norms in separable Banach spaces.Studia Math., to appear. MR 1398174
Reference: [3] Deville R., Godefroy G., Zizler V.: Smoothness and renormings in Banach spaces.Pitman Monographs and Surveys in Pure and Applied Mathematics 64, 1993. Zbl 0782.46019, MR 1211634
Reference: [4] Dugundji J.: Topology.Allyn and Bacon Inc., 1966. Zbl 0397.54003, MR 0193606
Reference: [5] Haydon R.: Normes infiniment differentiables sur certains espaces de Banach.C.R. Acad. Sci. Paris, t. 315, Serie I (1992), 1175-1178. Zbl 0788.46008, MR 1194512
Reference: [6] Haydon R.: Trees in renormings appear. MR 1674838


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