A note on extreme points of the intersection of operator segments (Q1175046)

Let \(B_ +(H)\) denote the set of all positive semidefinite bounded linear operators on a Hilbert space \(H\). For \(A\in B_ +(H)\), the operator segment \([0,A]\) consists of those \(T\in B_ +(H)\) with \(0 \leq T \leq A\). Let \(M[A,B]\) denote the intersection of operator segments \([0,A]\) and \([0,B]\). T. Ando has determined the extreme points of \(M[A,B]\) when \(dim H<\infty\). The present paper investigates what can be said when \(dim H=\infty\) and his results provide another proof of Ando's theorem. The notions of shorts of a given operator and the parallel sum of two operators in \(B_ +(H)\) are utilized.