$2$-rotundity of some nonseparable abstract interpolation spaces

Stephen Dilworth; Denka Kutzarova

$2$-rotundity of some nonseparable abstract interpolation spaces

Functional Analysis 2026-06-25 v1

Authors: Stephen Dilworth , Denka Kutzarova

Abstract

Generalizing a construction due to Argyros and Motakis \cite{AM}, we define a nonseparable abstract interpolation space associated to any given reflexive space with an unconditional basis together with the Schreier spaces associated to an increasing sequence of compact families of finite subsets of an uncountable set. Under a mild complexity assumption on the families, we prove that the interpolation space admits a $2$ -rotund norm with an uncountable $1$ -unconditional basis.

Keywords

abstract interpolation space nonseparable space unconditional basis schreier spaces 2-rotund norm reflexive space

Cite

@article{arxiv.2606.27473,
  title  = {$2$-rotundity of some nonseparable abstract interpolation spaces},
  author = {Stephen Dilworth and Denka Kutzarova},
  journal= {arXiv preprint arXiv:2606.27473},
  year   = {2026}
}