An approximation property with respect to an operator ideal

Juan Manuel Delgado¹ ; Cándido Piñeiro²

¹ Departamento de Matemática Aplicada I Escuela Técnica Superior de Arquitectura Avenida Reina Mercedes, 2 41012 Sevilla, Spain
² Departamento de Matemáticas Facultad de Ciencias Experimentales Campus Universitario del Carmen 21071 Huelva, Spain

Studia Mathematica, Tome 214 (2013) no. 1, pp. 67-75

Résumé

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.

Détail

DOI : 10.4064/sm214-1-4

Keywords: given operator ideal mathcal say banach space has approximation property respect mathcal belongs overline circ mathcal tau every banach space every mathcal tau being topology uniform convergence compact sets present several characterizations type approximation property shown existing approximation properties literature may included setting