# Article

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Keywords:
smooth norms; approximation; lattice norms; $c_0(\Gamma)$; $C_0[0, \omega_1]$
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 $C_0[0,\omega_1]$.
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