EXTREME POINTS OF INTERVAL BETWEEN 2 OPERATORS Academic Article

Given that A, B are operators on a complex Hilbert space, and that B A B - A is nonnegative, the interval between A and B consists of every operator, G, such that both B G B - G and G A G - A are nonnegative. The extreme points of such an interval are exhibited and the interval is shown to be the closure of the convex hull of these extreme points in the weak-operator topology.