Definition:Point Spectrum of Densely-Defined Linear Operator

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

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

We define the point spectrum $\map {\sigma_p} T$ as the set of $\lambda \in \C$ such that:


 * $T - \lambda I$ is not injective.

Also see

 * Definition:Point Spectrum of Bounded Linear Operator