This is an announcement for the paper “On the bounded approximation property on subspaces of $\ell_p$ when $0<p<1$ and related issues” by Félix Cabello Sánchezhttps://arxiv.org/search/math?searchtype=author&query=S%C3%A1nchez%2C+F+C, Jesús M. F. Castillohttps://arxiv.org/search/math?searchtype=author&query=Castillo%2C+J+M+F, Yolanda Morenohttps://arxiv.org/search/math?searchtype=author&query=Moreno%2C+Y.

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 $\ell_p\to X$ has the BAP when $X$ has it and $0<p\leq 1$, 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.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1808.03169