Bulletin of the
Korean Mathematical Society BKMS

Suppose $X$ is a closed subspace of $\sumX$, $\dim X_n$ $ < \infty$, which has the metric compact approximation property. It is proved that if $Y$ is a Banach space of cotype $q$ for some $2 \leq q < \infty$ then $K(X,Y)$ is an $M$-ideal in $L(X,Y)$.

Keywords: compact operator, M-ideal, cotype $q$, the metric compact approximation

MSC numbers: 46A32, 41A50