Definition:Spectrum (Spectral Theory)/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