M-ideals of compact operators into $\ell_p$

Abstract

We show for $2\le p<\infty$ and subspaces $X$ of quotients of $L_{p}$ with a $1$-unconditional finite-dimensional Schauder decomposition that $K(X,\ell_{p})$ is an $M$-ideal in $L(X,\ell_{p})$.