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A commutativity theorem for semibounded operators in hilbert space

Authors:	A Edward Nussbaum

Institution:	Department of Mathematics, Washington University, St. Louis, Missouri 63130

Abstract:	Let and be semibounded (bounded from below) operators in a Hilbert space $\mathfrak H$ and $\mathfrak D$ a dense linear manifold contained in the domains of , , , and , and such that for all in $\mathfrak D$ . It is shown that if the restriction of to $\mathfrak D$ is essentially self-adjoint, then and are essentially self-adjoint and $\bar A$ and $\bar B$ commute, i.e. their spectral projections permute.

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