English

Some remarks on smooth renormings of Banach spaces

Functional Analysis 2020-06-09 v3

Abstract

We prove that in every separable Banach space XX with a Schauder basis and a CkC^k-smooth norm it is possible to approximate, uniformly on bounded sets, every equivalent norm with a CkC^k-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