Category:Residual Spectra (Densely-Defined Linear Operators)

This category contains results about residual spectrums in the context of Densely-Defined Linear Operators.
Definitions specific to this category can be found in Definitions/Residual Spectra (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.

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

$T - \lambda I$ is injective but $\map {\paren {T - \lambda I} } {\map D T}$ is not everywhere dense in $\HH$.