Formally Normal Operators Having no Normal Extensions

Abstract

The domain and null space of an operator A in a Hilbert space will be denoted by and , respectively. A formally normal operator N in is a densely defined closed (linear) operator such that , and for all A normal operator in is a formally normal operator N satisfying 35 . A study of the possibility of extending a formally normal operator N to a normal operator in the given , or in a larger Hilbert space, was made in (1).