Added the unitisation.

This commit is contained in:
Bokuan Li
2026-06-04 13:39:55 -04:00
parent 6441352421
commit ebead6c022
3 changed files with 56 additions and 4 deletions

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@@ -19,7 +19,6 @@
\label{proposition:gelfand-transform-gymnastics}
Let $A$ be a commutative unital Banach algebra and $x \in A$, then:
\begin{enumerate}
\item $\Gamma_A$ is a contractive homomorphism.
\item $\Gamma_A(1) = 1$.
\item $x \in G(A)$ if and only if $\Gamma_A x \in G(C(\Omega(A); \complex))$.
\item $(\Gamma_Ax)(\Omega(A)) = \sigma_A(x)$.