A note on lattice renormings

Marián J. Fabián; Petr Hájek; Václav Zizler

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 2, page 263-272
  • ISSN: 0010-2628

Abstract

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It is shown that every strongly lattice norm on c 0 ( Γ ) can be approximated by C ∞ smooth norms. We also show that there is no lattice and Gâteaux differentiable norm on C 0 [ 0 , ω 1 ] .

How to cite

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Fabián, Marián J., Hájek, Petr, and Zizler, Václav. "A note on lattice renormings." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 263-272. <http://eudml.org/doc/248101>.

@article{Fabián1997,
abstract = {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 Gâteaux differentiable norm on $C_0[0,\omega _1]$.},
author = {Fabián, Marián J., Hájek, Petr, Zizler, Václav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {smooth norms; approximation; lattice norms; $c_0(\Gamma )$; $C_0[0, \omega _1]$; smooth norms; approximation; lattice norms},
language = {eng},
number = {2},
pages = {263-272},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on lattice renormings},
url = {http://eudml.org/doc/248101},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Fabián, Marián J.
AU - Hájek, Petr
AU - Zizler, Václav
TI - A note on lattice renormings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 2
SP - 263
EP - 272
AB - 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 Gâteaux differentiable norm on $C_0[0,\omega _1]$.
LA - eng
KW - smooth norms; approximation; lattice norms; $c_0(\Gamma )$; $C_0[0, \omega _1]$; smooth norms; approximation; lattice norms
UR - http://eudml.org/doc/248101
ER -

References

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  1. Deville R., Fonf V., Hájek P., Analytic and polyhedral approximations of convex bodies in separable polyhedral Banach spaces, Israel J. Math., to appear. MR1639743
  2. Deville R., Fonf V., Hájek P., Analytic and C k -smooth approximations of norms in separable Banach spaces, Studia Math., to appear. MR1398174
  3. Deville R., Godefroy G., Zizler V., Smoothness and renormings in Banach spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics 64, 1993. Zbl0782.46019MR1211634
  4. Dugundji J., Topology, Allyn and Bacon Inc., 1966. Zbl0397.54003MR0193606
  5. Haydon R., Normes infiniment differentiables sur certains espaces de Banach, C.R. Acad. Sci. Paris, t. 315, Serie I (1992), 1175-1178. Zbl0788.46008MR1194512
  6. Haydon R., Trees in renormings theory, to appear. MR1674838

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