Some duality results on bounded approximation properties of pairs
Volume 217 / 2013
Studia Mathematica 217 (2013), 79-94
MSC: Primary 46B28; Secondary 46B20, 46B10, 47B10.
DOI: 10.4064/sm217-1-5
Abstract
The main result is as follows. Let $X$ be a Banach space and let $Y$ be a closed subspace of $X$. Assume that the pair $(X^{*}, Y^{\perp })$ has the $\lambda $-bounded approximation property. Then there exists a net $( S_\alpha )$ of finite-rank operators on $X$ such that $S_\alpha (Y) \subset Y$ and $\| S_\alpha \| \leq \lambda $ for all $\alpha $, and $( S_\alpha )$ and $( S^{*}_\alpha )$ converge pointwise to the identity operators on $X$ and $X^{*}$, respectively. This means that the pair $(X,Y)$ has the $\lambda $-bounded duality approximation property.
