Triangulating chains of projections and completely non-selfadjoint parts of linear operators (Q1842479)

A family \(P\) of orthogonal projections in a separable Hilbert space \(H\), ordered by inclusion and containing \(O\) and \(I\) is called a chain. The authors define various properties of such a chain relative to a bounded linear operator \(A\) of \(H\) into \(H\) with real spectrum \(\sigma(A)\subset \mathbb{R}\). They show that various properties of \(A\) imply corresponding relations among the properties of \(P\) relative to \(A\) referred to above. They also consider the case in which \(\sigma(A)\) need not be real in which properties of \(P\) imply properties of \(A\).