On the weak operator Daugavet property and poor subspaces

Samir Hamad

On the weak operator Daugavet property and poor subspaces

Functional Analysis 2026-08-11 v1

Authors: Samir Hamad

Abstract

We will provide an example of a Banach space with the Daugavet property which does not possess the weak operator Daugavet property. We will also show that every separable Banach space with the Daugavet property contains a non-poor subspace isomorphic to $\ell^1$ while noticing that every separable subspace of $L^\infty[0,1]$ is poor.

Keywords

Daugavet property weak operator Daugavet property poor subspaces Banach spaces separable spaces

Cite

@article{arxiv.2608.11098,
  title  = {On the weak operator Daugavet property and poor subspaces},
  author = {Samir Hamad},
  journal= {arXiv preprint arXiv:2608.11098},
  year   = {2026}
}