Definition 41.2.9 (Numerical Radius).label Let $H$ be a complex Hilbert space and $T \in B(H)$, then
\[w(T) = \sup_{\substack{\xi \in H \\ \norm{\xi}_H = 1}}|\dpn{T\xi, \xi}{H}|\]
is the numerical radius of $T$.
Definition 41.2.9 (Numerical Radius).label Let $H$ be a complex Hilbert space and $T \in B(H)$, then
is the numerical radius of $T$.
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