A commutativity theorem for semibounded operators in hilbert space
Authors:
A. Edward Nussbaum
Affiliation:
Department of Mathematics, Washington University, St. Louis, Missouri 63130
Abstract:
Let and be semibounded (bounded from below) operators in a Hilbert space and a dense linear manifold contained in the domains of , , , and , and such that for all in . It is shown that if the restriction of to is essentially self-adjoint, then and are essentially self-adjoint and and commute, i.e. their spectral projections permute.