Minimal and Maximal Operator Theory With Applications

Source abstract

Abstract Let X be a complex Banach space and A a linear operator from X into X with dense domain. We construct the minimal and maximal operators of the operator A and prove that they are equal under reasonable hypotheses on the space X and operator A . As an application, we obtain the existence and regularity of weak solutions of linear equations on the space X . As another application we obtain a criterion for a symmetric operator on a complex Hilbert space to be essentially self-adjoint. An application to pseudo-differential operators of the Weyl type is given.