An approximation property with respect to an operator ideal
Volume 214 / 2013
Studia Mathematica 214 (2013), 67-75
MSC: Primary 46B28; Secondary 47L20, 46B50.
DOI: 10.4064/sm214-1-4
Abstract
Given an operator ideal ${\mathcal A}$, we say that a Banach space $X$ has the approximation property with respect to ${\mathcal A}$ if $T$ belongs to $\overline {\{S\circ T: S\in {\mathcal F}(X)\}}^{\tau _c}$ for every Banach space $Y$ and every $T\in {\mathcal A}(Y,X)$, $\tau _c$ being the topology of uniform convergence on compact sets. We present several characterizations of this type of approximation property. It is shown that some of the existing approximation properties in the literature may be included in this setting.
