ScalingStacks

Definition 2.74. Let $\mathcal{A}$ and $\mathcal{B}$ be Banach $k$-algebras, and $\phi:\mathcal{A}\to\mathcal{B}$ be a homomorphism of Banach algebras. The spectrum of homomorphism $\phi$ is the image of $\mathfrak{M}(\mathcal{B})$ in $\mathfrak{M}(\mathcal{A})$ under $\phi^{\star}$. Denote it by $\Sigma_{\phi}$