On the numerical range of an operator
Ching-Hwa Meng · Proceedings of the American Mathematical Society · 1963
The numerical range of an operator P in a Hubert space is defined as the set of all the complex numbers (Tx, x), where x is a unit vector in the space.It is well known that a bounded normal operator has the property that the closure of its numerical range is exactly the convex hull of its spectrum [5, pp.325-327, Theorem 8.13 and Theorem 8.14].Call this property A. In this article let P denote a linear bounded operator in a Hilbert space H, V(T) be its numerical range, K(T) be the convex hull of its spectrum, and use the usual notations p(T),