English

Octahedrality and G\^ateaux smoothness

Functional Analysis 2024-08-08 v1

Abstract

We prove that every Banach space admitting a Gateaux smooth norm and containing a complemented copy of 1\ell_1 has an equivalent renorming which is simultaneously G\^ateaux smooth and octahedral. This is a partial solution to a problem from the early nineties.

Keywords

Cite

@article{arxiv.2408.03737,
  title  = {Octahedrality and G\^ateaux smoothness},
  author = {Ch. Cobollo and P. Hájek},
  journal= {arXiv preprint arXiv:2408.03737},
  year   = {2024}
}