Definition:Spectrum (Spectral Theory)/Unital Algebra

Definition
Let $A$ be a unital algebra over $\C$.

Let $x \in A$.

Let $\map {\rho_A} x$ be the resolvent set of $x$ in $A$.

We define the spectrum of $x$, $\map {\sigma_A} x$, by:
 * $\map {\sigma_A} x = \C \setminus \map {\rho_A} x$