# Remarks on M-ideals of compact operators

• Published : 1996.08.01

#### Abstract

A closed subspace J of a Banach space X is called an M-ideal in X if the annihilator $J^\perp$ of J is an L-summand of $X^*$. That is, there exists a closed subspace J' of $X^*$ such that $X^* = J^\perp \oplus J'$ and $\left\$\mid$p + q \right\$\mid$= \left\$\mid$p \right\$\mid$+ \left\$\mid$q \right\$\mid wherever $p \in J^\perp and q \in J'$.