Trees, linear orders and G\^ateaux smooth norms
Functional Analysis
2022-06-14 v1
Abstract
We introduce a linearly ordered set Z and use it to prove a necessity condition for the existence of a G\^ateaux smooth norm on C(T), where T is a tree. This criterion is directly analogous to the corresponding equivalent condition for Fr\'echet smooth norms. In addition, we prove that if C(T) admits a G\^ateaux smooth lattice norm then it also admits a lattice norm with strictly convex dual norm.
Keywords
Cite
@article{arxiv.0710.4230,
title = {Trees, linear orders and G\^ateaux smooth norms},
author = {Richard J. Smith},
journal= {arXiv preprint arXiv:0710.4230},
year = {2022}
}
Comments
A different version of this paper is to appear in J. London Math. Soc