The extreme points of a set of positive semidefinite operators (Q1110621)

Given a positive definite operator A and a subspace \({\mathcal S}\), the authors consider the operator interval \({\mathcal M}(A,{\mathcal S})=\{X:\) \(0\leq X\leq A\), range \(X\subset {\mathcal S}\}\). The supremum of this convex set is called the shorted operator \({\mathcal S}(A)\). The operators \({\mathcal S}(A)\), for the various subspaces \({\mathcal S}\), are identified with the extreme and exposed points of the set \({\mathcal M}(A)=\{X:\) \(0\leq X\leq A\}\).