Some remarks on smooth renormings of Banach spaces
Functional Analysis
2020-06-09 v3
Abstract
We prove that in every separable Banach space with a Schauder basis and a -smooth norm it is possible to approximate, uniformly on bounded sets, every equivalent norm with a -smooth one in a way that the approximation is improving as fast as we wish on the elements depending only on the tail of the Schauder basis. Our result solves a problem from the recent monograph of Guirao, Montesinos and Zizler.
Keywords
Cite
@article{arxiv.1705.01384,
title = {Some remarks on smooth renormings of Banach spaces},
author = {Petr Hájek and Tommaso Russo},
journal= {arXiv preprint arXiv:1705.01384},
year = {2020}
}
Comments
13 pp