I have a quick question, If $E$ is a Banach space and $H$ is a closed subspace of $E$, could we affirm this proposition:
If exists a linear continuous function $S:E\to H$ such that $S\circ i =Id_{_H}$ (with $i:H\hookrightarrow E$), then $H$ is complemented in $E$.
I don't need the proof, simply I need to know if this is true or false, thanks.