Category:Approximate Eigenvalues (Densely-Defined Linear Operators)

This category contains results about approximate eigenvalues in the context of Densely-Defined Linear Operators.
Definitions specific to this category can be found in Definitions/Approximate Eigenvalues (Densely-Defined Linear Operators).

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

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

Let $\lambda \in \C$.

We say that $\lambda$ is an approximate eigenvalue if and only if:

there exists a sequence $\sequence {x_n}_{n \mathop \in \N}$ in $\map D T$ such that:

$\paren {T - \lambda I} x_n \to 0$