Schauder bases and the bounded approximation property in separable Banach spaces

Abstract

Let $E$ be a separable Banach space with the $\lambda$-bounded approximation property. We show that for each $\epsilon >0$ there is a Banach space $F$ with a Schauder basis such that $E$ is isometrically isomorphic to a $1$-complemented subspace of $F$ an