Unbounded generalizations of the Fuglede-Putnam theorem and applications to the commutativity of self-adjoint operators (2201.10604v1)

Abstract: In this article, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem. As applications, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded closed symmetric operator.