Category:Spectra (Densely-Defined Linear Operators)

This category contains results about spectra in the context of densely-defined linear operators.
Definitions specific to this category can be found in Definitions/Spectra (Densely-Defined Linear Operators).

Let $\HH$ be a Hilbert space over $\C$.

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

Let $\map \rho T$ be the resolvent set of $\struct {\map D T, T}$.

We define the the spectrum of $T$, $\map \sigma T$, by:

$\map \sigma T = \C \setminus \map \rho T$