I know that given a closed subspace $M$ of a Hilbert space $H$, we can find a closed omplement $N$ of $M$ such that $H=M\oplus N$. I was trying to see when this property holds for Banach spaces too.
Coming to the question, given $c_0$, the space of complex sequences converging to zero, looked upon as a closed subspace of $(l^\infty, |. |_\infty)$, does there exist such a complement? If no, why not? And if yes, can it be explicitly described?
