Extreme points of the intersection and the union of some operator balls

The extreme points of the set {A: A * A <= R^2,AA* <= R^2} of operators acting in the n-dimensional Euclidean space are investigated. For n=2 a complete description of this set is given. For the set {A: A * A<= R^2} (union) {A: AA* <= R^2} the extreme points are described for all n.