An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property

Abstract

C.-M. Cho and W. B. Johnson showed that if a subspace E of $ℓ_p$, 1 < p < ∞, has the compact approximation property, then K(E) is an M-ideal in ℒ(E). We prove that for every r,s ∈ ]0,1] with $r^2 + s^2 < 1$, the James space can be provided with an equival