Hello, I'd like some help to find an answer I've been looking for since this morning. Let $X$ be a Banach space and let $Y$ be an $n$-codimensional subspace of $X$. Let $P$ be a projection from $X$ onto $Y$. Which is the best estimate for the norm of $P$? I found this information in an article by Bohnenblust as far as $n=1$ is concerned (that is, there always exists a projection $P$ such that $\|P\|\leq 2+\varepsilon$), but nothing satisfactory when the codimension increases. Thank you.