### A classification of projectors

A positive operator A and a closed subspace of a Hilbert space ℋ are called compatible if there exists a projector Q onto such that AQ = Q*A. Compatibility is shown to depend on the existence of certain decompositions of ℋ and the ranges of A and ${A}^{1/2}$. It also depends on a certain angle between A() and the orthogonal of .