diff --git a/src/op/banach/spectrum.tex b/src/op/banach/spectrum.tex index 2051d37..40964ca 100644 --- a/src/op/banach/spectrum.tex +++ b/src/op/banach/spectrum.tex @@ -69,8 +69,8 @@ which tends to $0$ as $|\lambda| \to \infty$, $R_x \in H(\complex; A) \cap C_0(\complex; A)$. By \hyperref[Liouville's Theorem]{theorem:liouville}, $R_x = 0$, which is impossible. \end{proof} -\begin{theorem}[Gelfand-Naimark] -\label{theorem:gelfand-naimark} +\begin{theorem}[Gelfand-Mazur] +\label{theorem:gelfand-mazur} Let $A$ be a unital Banach algebra. If every non-zero element of $A$ is invertible, then $A$ is isometrically isomorphic to $\complex$. \end{theorem} \begin{proof}