Definition:Spectrum of Bounded Linear Operator

Definition
Let $\struct {X, \norm \cdot_X}$ be a Banach space over $\C$.

Let $A : X \to X$ be a bounded linear operator.

Let $\map \rho A$ be the resolvent set of $A$.

Let:


 * $\map \sigma A = \C \setminus \map \rho A$

We say that $\map \sigma A$ is the spectrum of $A$.

Also see

 * Definition:Point Spectrum of Linear Operator