English

The weak Banach-Saks property for H\"older spaces

Functional Analysis 2026-03-04 v1

Abstract

We investigate the weak Banach--Saks property in the setting of H\"older spaces over metric spaces. We show that, for every infinite metric space (M,d)(M,d) and every α(0,1]\alpha \in (0,1], the H\"older space Cα(M)C^{\alpha}(M) fails to have the weak Banach--Saks property.

Keywords

Cite

@article{arxiv.2603.02977,
  title  = {The weak Banach-Saks property for H\"older spaces},
  author = {Prezemysław Górka and Mauro Sanchiz},
  journal= {arXiv preprint arXiv:2603.02977},
  year   = {2026}
}