Definition:Numerical Range of Hermitian Operator

Definition

Let $\GF \in \set {\R, \C}$.

Let $\struct {\HH, \innerprod \cdot \cdot}$ be a Hilbert space over $\GF$.

Let $T : \HH \to \HH$ be a Hermitian operator.

We define the numerical range $\map V T$ by:

$\map V T = \set {\innerprod {T x} x : x \in \HH, \, \norm x = 1}$

Sources

• 2020: James C. Robinson: Introduction to Functional Analysis ... (previous) ... (next) $16.1$: Eigenvalues of Self-Adjoint Operators