Definition:Spectral Radius/Bounded Linear Operator
< Definition:Spectral Radius(Redirected from Definition:Spectral Radius of 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
- 2002: Peter D. Lax: Functional Analysis: $17.1$: Normed Algebras