POLYNOMIALS OF UNBOUNDED POSITIVE SELF-ADJOINT OPERATORS

Abstract

The polynomials of unbounded Self-adjoint operators are not necessarily Self-adjoint because as much as their terms may be densely defined, the sum of the terms may not be densely defined. In this paper, we provide the conditions under which the polynomials may be Self-adjoint. This is an extension of the results by Mortad on the sum of two densely defined unbounded Self-adjoint operators. We achieve this by limiting the choice of our operators to invertible unbounded self adjoint operators in which strictly positive unbounded Self-adjoint operators are part of.