English

On the bounded approximation property on subspaces of $\ell_p$ when $0<p<1$ and related issues

Functional Analysis 2018-08-10 v1

Abstract

This paper studies the bounded approximation property (BAP) in quasi Banach spaces. In the first part of the paper we show that the kernel of any surjective operator pX\ell_p\to X has the BAP when XX has it and 0<p10<p\leq 1, which is an analogue of the corresponding result of Lusky for Banach spaces. We then obtain and study nonlocally convex versions of the Kadec-Pe\l czy\'nski-Wojtaszczyk complementably universal spaces for Banach spaces with the BAP.

Keywords

Cite

@article{arxiv.1808.03169,
  title  = {On the bounded approximation property on subspaces of $\ell_p$ when $0<p<1$ and related issues},
  author = {Félix Cabello Sánchez and Jesús M. F. Castillo and Yolanda Moreno},
  journal= {arXiv preprint arXiv:1808.03169},
  year   = {2018}
}