Intersection properties of ball sequences and uniqueness of Hahn-Banach extensions

Let X be a Banach space and Y a closed subspace. We introduce an intrinsic geometric property of Y-the k-ball sequence property-which is a weakening o f the famous k-ball property due to Alfsen & Effros. We prove that Y satisf ies the 2-ball sequence property if and only if Y has the Phelps uniqueness property U (i.e. every continuous linear functional g is an element of Y* has a unique norm-preserving extension f is an element of X*). We prove tha t Y is an ideal having property U if and only if Y satisfies the k-ball seq uence property, and in this case, Y satisfies the k-ball sequence property for all k.