ScalingStacks

Proposition 2.57. Let $\mathcal{A}$ be a reduced strict affinoid algebra. Then its spectral norm $\vvvert\mathord{\cdot}\vvvert_{\mathcal{A},\text{sp}}$ is a complete norm on $\mathcal{A}$. It is equivalent to the Banach algebra norm $\vvvert\mathord{\cdot}\vvvert_{\mathcal{A}}$. ([FvdP, Theorem 3.4.9], [BGR, Theorem 6.2.4.1])