Proposition 2.30 . [00I2]

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Proposition 2.30.

Let $\mathcal{A}$ be a $k$ -Banach algebra. For any $f\in A$ , one has ([Ber, Theorem 1.3.1])

\vvvert f\vvvert_{\mathrm{sp}}=\max_{z\in\mathfrak{M}(A)}|f|_{z}