Definition:Spectrum (Spectral Theory)/Bounded Linear Operator
< Definition:Spectrum (Spectral Theory)(Redirected from Definition:Spectrum 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 $\map \rho A$ 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
- Results about spectra of bounded linear operators can be found here.
Sources
- 2020: James C. Robinson: Introduction to Functional Analysis ... (previous) ... (next) $14.1$: The Resolvent and Spectrum