Bulletin of the
Korean Mathematical Society BKMS

Suppose $X$ and $Y$ are Banach spaces for which $K(X,Y)$, the space of compact operators from $X$ to $Y$, is an M-ideal in $L(X,Y)$, the space of bounded linear operators from $X$ to $Y$. If $Z$ is a closed subspace of $Y$ such that $L(X,Z)$ has property SU in $L(X,Y)$ and $d(T, K(X,Z)) = d(T, K(X,Y))$ for all $T \in L(X,Z)$, then $K(X,Z)$ is an M-ideal in $L(X,Z)$ if and only if it has property SU in $L(X,Z)$.

Keywords: M-ideal, HB-subspace, property SU, property U, compact operator

MSC numbers: 46B20, 46B28