I want to show $c_0$ is not reflexive by showing the canonical embedding $T:c_0\rightarrow c_0^{**}$ is not surjective.
And I know $c_0$ is a closed subspace of $\ell_\infty$ and $\ell_\infty$ is isometrically isomorphic to $c_0^{**}$. But I couldn't find $x^{**}\in c_0^{**}$ such that $T(x)\neq x^{**}$ ($x\in c_0$). Can anyone help me to show the canonical embedding $T:c_0\rightarrow c_0^{**}$ is not surjective?
Thank you!