i am not sure how to proceed about the following exercise.
Let $E$ be a normed vectorial space. Let $p$ be a projection of $E$ (i.e $p \circ p=p) $. Show that the application from $ F \times G$ into $E$ where $F=Ker(p)$ and $G=range(p)$ such that ,$u(x,y)=x+y$ is an isomorphism.
We proved just before that $F,G$ are closed in $E$.
Not sure about what i should use, the fact that $E$ and $F,G$ are in direct sum ? Should i work with $(p(u(x,y))$ ? Thanks!