Definition:Spectral Radius/Bounded Linear Operator

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Definition

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

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

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


The spectral radius of $A$ is defined as:

$\ds \size {\map \sigma A} := \sup_{z \mathop \in \map \sigma A} \cmod z$


Sources