Banach algebra $l^p$ is not isomorphic to $C^{*}$ algebra

Question

Consider commutative Banach algebra $l^p$, $p \in [1,\infty)$ with multiplication by coordinates. I know, that $\Delta (l^{p})=\{e_n : n \in \mathbb{N}\}$ - set of canonical functionals. We know that $\widehat{x}(e_n)=x_n$ and $\widehat{x}: l^{p} \to C_0(\Delta (l^{p}))$. Because there exists $x\in l^{p}$ such that $x_i\neq x_j$ for $i\neq j$, and Gelfand transformation is continuous, GT must be discrete. I would like to show, that GT is or is not surjective, but I do not have any idea. Many thanks