Let $T$ be an operator on a Hilbert space $\mathcal{H}$, and recall that the numerical range of $T$ is defined as $W(T) = \{\langle Tx,x \rangle \mid ||x|| = 1\}$. Here is a theorem I'm reading:
If $\lambda \in W(T)$ is a boundary point at which $\partial W(T)$ has infinite curvature, then $\lambda$ is an eigenvalue of $T$.
Question: What exactly does it mean for $\partial W(T)$ to have infinite curvature at $\lambda$?