Previous |  Up |  Next


smooth norms; approximation; lattice norms; $c_0(\Gamma)$; $C_0[0, \omega_1]$
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 $C_0[0,\omega_1]$.
[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
[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
[3] Deville R., Godefroy G., Zizler V.: Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys in Pure and Applied Mathematics 64, 1993. MR 1211634 | Zbl 0782.46019
[4] Dugundji J.: Topology. Allyn and Bacon Inc., 1966. MR 0193606 | Zbl 0397.54003
[5] Haydon R.: Normes infiniment differentiables sur certains espaces de Banach. C.R. Acad. Sci. Paris, t. 315, Serie I (1992), 1175-1178. MR 1194512 | Zbl 0788.46008
[6] Haydon R.: Trees in renormings theory. to appear. MR 1674838
Partner of
EuDML logo