On the bounded approximation property on subspaces of ℓp when 0 < p < 1 and related issues-Reference-Cited by-同舟云学术

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

Published:2019-11-01 Issue:6 Volume:31 Page:1533-1556
ISSN:1435-5337
Container-title:Forum Mathematicum
language:
Short-container-title:

Author:

Cabello Sánchez Félix¹,Castillo Jesús M. F.¹,Moreno Yolanda²

Affiliation:

1. Instituto de Matemáticas, Universidad de Extremadura, Avenida de Elvas s/n, 06071Badajoz, Spain

2. Instituto de Matemáticas, Universidad de Extremadura, Escuela Politécnica, Avenida de la Universidad s/n, 10071Cáceres, Spain

Abstract

AbstractThis 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–Pełczyński–Wojtaszczyk complementably universal spaces for Banach spaces with the BAP.

Funder

Dirección General de Investigación Científica y Técnica

Consejería de Educación y Empleo, Junta de Extremadura

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2018-0174/pdf

Reference52 articles.

1. On the bounded approximation property in Banach spaces;Israel J. Math.,2013

2. Some approximation properties of Banach spaces and Banach lattices;Israel J. Math.,2011