Vol. 4 No. 4 April, 2019
ON THE DERTERMINATION OF EXTENSIONS OF CLOSABLE OPERATORS AND THE NUMERICAL RANGE
Abstract
The study of extensions of densely defined operators has led to operators whose image have a real part that is contained wholly in the left hand side of the imaginary line of the complex plane. This is achieved through the fact that when the numerical range of a sesquilinear operator, is not the whole plane, then it is contained in the half plane and is given by