Category:Numerical Range

This category contains results about Numerical Range.
Definitions specific to this category can be found in Definitions/Numerical Range.

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

Let $\norm {\, \cdot \,}$ be the inner product norm on $\struct {\HH, \innerprod \cdot \cdot}$.

Let $\struct {\map D T, T}$ be a densely-defined linear operator on $\HH$.

We define the numerical range $\map W T$ of $T$ by:

$\map W T = \set {\innerprod {T u} u : u \in \map D T, \, \norm u = 1}$