Centers of symmetry in finite intersections of balls in Banach spaces

It is proved that a real Banach spaceX is aG-space (C _σ - space)if and only if the non-empty intersection of three balls with equal radii (any three balls) has a center of symmetry.     

The metric approximation property,norm-one projections and intersection properties of balls

We show that ifE is a Banach space with the Radon-Nikodym property thenE has the metric approximation property if and only if the space of finite rank operators is locally complemented in the space of bounded operators.