# A proof of the ordinary Gleason-Kahane-Żelazko theorem for complex functionals

Desvl at
The Theorem(Gleason-Kahane-Żelazko) If $\phi$ is a complex linear functional on a unitary Banach algebra $A$, such that $\phi(e)=1$ and $\phi(x) \neq 0$ for every invertible $x \in A$, then\phi(xy)=\phi(x)\phi(y)Namely, $\phi$ is a complex homomorphism. Notations and remarksSuppose $A$ is a complex ……