Approximation properties of pairs of subspaces
Bull. Korean Math. Soc.
Published online 2019 May 16
Keun Young Lee
Sejong University
Abstract : The paper is concerned with approximation properties of pairs. For $\lambda \geq 1$, we prove that given a Banach space $X$ and closed subspace $Z_{0}$, the pair $(X,Z_{0})$ has the $\lambda$-bounded approximation property
($\lambda$-BAP) if and only if for every ideal $Z$ containing $Z_{0}$, the pair $(Z,Z_{0})$ has the $\lambda$-BAP
and that if $Z$ is a closed subspace of $X$ and the pair $(X,Z)$ has the $\lambda$-BAP, then every separable subspace $Y_{0}$ of $X$, there exists a separable subspace $Y$ containing $Y_{0}$ such that the pair $(Y,Y\cap Z)$ has the $\lambda$-BAP. We also provide that if $Z$ be a separable closed subspace of $X$, then the pair $(X,Z)$ has the $\lambda$-BAP if and only if every separable subspace $Y_{0}$ of $X$, there exists a separable subspace $Y$ containing $Y_{0}$ and $Z$ such that the pair $(Y,Z)$ has the $\lambda$-BAP.
Keywords : bounded approximation property of pairs, approximation property of pairs, ideals
MSC numbers : 46B28; 47L20
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang.co., Ltd