  Based on the success of a well-known method for solving higher order linear
differential equations, a study of two of the most important mathematical
features of that method, viz. the null spaces and commutativity of the product
of unbounded linear operators on a Hilbert space is carried out. A principle is
proved describing solutions for the product of such operators in terms of the
solutions for each of the factors when the null spaces of those factors satisfy
a certain geometric relation to one another. Another geometric principle
equating commutativity of a closed densely defined operator and a projection to
stability of the range of the projection under the closed operator is proved.
