Gelfand's Spectral Radius Formula/Bounded Linear Operator

Theorem
Let $\struct {X, \norm \cdot _X}$ be a Banach space over $\C$.

Let $\map B X$ be the set of bounded linear operators on $X$.

Let $\norm \cdot_{\map B X}$ denote the operator norm on $\map B X$.

Let $T \in \map B X$.

Let $\size {\map \sigma T}$ be the spectral radius of $T$.

Then:
 * $\ds \size {\map \sigma T} = \lim_{n \to \infty} \paren {\norm{T^n}_{\map B X} }^{1/n}$