Definition:Spectral Radius/Bounded Linear Operator

Definition
Let $\mathbb F \in \set {\R, \C}$.

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

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

Let $\map \sigma A$ be the spectrum of $A$.

The spectral radius of $A$ is defined as:
 * $\ds \size {\map \sigma A} := \sup_{z \mathop \in \map \sigma A} \cmod z$