Is correct say that $(\ell_\infty)'\subset (c_0)'$?
My idea is the following:
I know that $c_0\subset\ell_\infty$. Then, the function $$ \begin{split} \Psi:(\ell_\infty)'&\to(c_0)'\\ f&\mapsto\Psi(f)=f|_{c_0} \end{split} $$ is injective.
Is correct the function? Does exist an injective function $\Psi$ such that $(\ell_\infty)'\subset (c_0)'$?