Isomorphism between bilinear function space and linear function spaces

Question

$E$, $F$ and $G$ are three vector spaces on $\mathbb{R}$. $L_2(E\times F; G)$ is the space of bilinear applications and $L(E; F)$ the space of linear applications. Could you indicate me a simple isomorphism between $L_2 (E\times F; G)$ and $L (E; L(F; G))$?

Answer 1

$B\mapsto \left( x \mapsto \left( y \mapsto B(x,y) \right) \right)$, the inverse being $L \mapsto \left( (x,y) \mapsto (L(x))(y) \right)$. Note that the both are canonically isomorphic to $L(E\otimes_k F ; G)$.