# The metric approximation property and intersection properties of balls

• Published : 1994.08.01

#### Abstract

In 1983 Harmand and Lima [5] proved that if X is a Banach space for which K(X), the space of compact linear operators on X, is an M-ideal in L(X), the space of bounded linear operators on X, then it has the metric compact approximation property. A strong converse of the above result holds if X is a closed subspace of either $\elll_p(1 < p < \infty) or c_0 [2,15]$. In 1979 J. Johnson [7] actually proved that if X is a Banach space with the metric compact approximation property, then the annihilator K(X)^\bot$of K(X) in$L(X)^*$is the kernel of a norm-one projection in$L(X)^*\$, which is the case if K(X) is an M-ideal in L(X).