Proposition 7.4.9 (Mutliplicative Linear Functionals).label Let $A$ be a unital Banach algebra then a linear functional $\p:A\to \com$ is multiplicative that is $\p(xy)=\p(x)\p(y)$ for all $x,y\in A$ if and only if

• $\p(1)=1$

• $\p(x)\neq 0$ whenever $x\in A$ is invertible