Trees, Linear Orders and Gâteaux Smooth Norms
نویسنده
چکیده
We introduce a linearly ordered set Z and use it to prove a necessity condition for the existence of a Gâteaux smooth norm on C0(Υ), where Υ is a tree. This criterion is directly analogous to the corresponding equivalent condition for Fréchet smooth norms. In addition, we prove that if C0(Υ) admits a Gâteaux smooth lattice norm then it also admits a lattice norm with strictly convex dual norm.
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