Approximation properties of tensor norms and operator ideals for Banach spaces

Abstract

For a finitely generated tensor norm α\alpha , we investigate the α\alpha -approximation property (α\alpha -AP) and the bounded α\alpha -approximation property (bounded α\alpha -AP) in terms of some approximation properties of operator ideals. We prove that a Banach space X has the λ\lambda -bounded αp,q{\alpha }_{p,q}-AP (1≤p,q≤∞,1/p+1/q≥1)(1\le p,q\le \infty ,1/p+1/q\ge 1) if it has the λ\lambda -bounded gp{g}_{p}-AP. As a consequence, it follows that if a Banach space X has the λ\lambda -bounded gp{g}_{p}-AP, then X has the λ\lambda -bounded wp{w}_{p}-AP.

Keywords

• approximation property
• tensor norm
• banach operator ideal
• 46b28
• 46b45
• 47l20