Page "Banach algebra" Paragraph 31
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Unital Banach algebras over the complex field provide a general setting to study spectral theory.
The spectrum of an element x ∈ A, denoted by, consists of all those complex scalars λ such that x − λ1 is not invertible in A.
The spectrum of any element x is a closed subset of the closed disc in C with radius || x || and center 0, and thus is compact.
Moreover, the spectrum of an element x is non-empty and satisfies the spectral radius formula:
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