Definition:Point Spectrum of Densely-Defined Linear Operator/Eigenvalue

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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 say that $\lambda \in \C$ is an eigenvalue of $T$ if and only if there exists $x \in \map D T \setminus \set 0$ such that:

$T x = \lambda x$


Also see


Sources