Solution
= Solution
\b[Yes.] For $x=(x_n)\in c$, let $L=\lim_nx_n$ and define
$$
T(x)=(L,x_1-L,x_2-L,\ldots).
$$
The tail tends to zero, so $T(x)\in c_0$, and $\lVert T(x)\rVert_\infty\leq2\lVert x\rVert_\infty$. Conversely, for $y=(y_n)\in c_0$, define
$$
T^{-1}(y)_n=y_1+y_{n+1}.
$$
This <sequence> converges to $y_1$ and has norm at most $2\lVert y\rVert_\infty$. The formulas are inverse bounded <linear maps>, so $c$ and $c_0$ are isomorphic Banach spaces.