# 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

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topFabián, 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

top- Deville R., Fonf V., Hájek P., Analytic and polyhedral approximations of convex bodies in separable polyhedral Banach spaces, Israel J. Math., to appear. MR1639743
- Deville R., Fonf V., Hájek P., Analytic and ${C}^{k}$-smooth approximations of norms in separable Banach spaces, Studia Math., to appear. MR1398174
- 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
- Dugundji J., Topology, Allyn and Bacon Inc., 1966. Zbl0397.54003MR0193606
- Haydon R., Normes infiniment differentiables sur certains espaces de Banach, C.R. Acad. Sci. Paris, t. 315, Serie I (1992), 1175-1178. Zbl0788.46008MR1194512
- Haydon R., Trees in renormings theory, to appear. MR1674838

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