Let $E,F$ be operator spaces and $K$ be a Hilbert space. Let $E\otimes_{h}F$ denote the Haagerup tensor product of $E$ and $F$.
Defnition 1. A bilinear map $u:E\times F\rightarrow B(K)$ is said to be 'Completely bounded' if the associated map $\tilde{u}:E\otimes_{h}F\rightarrow B(K)$ is completely bounded. In this case we define $\|u\|_{cb}=\|\tilde{u}\|_{cb}$.
Definition 2. $u$ is said to be 'Jointly completely bounded' In if for any operator spaces $B_{1}$ and $B_{2}$, $u$ can be boundedly extended to a bilinear map $(u)_{B_{1},B_{2}}:E\otimes_{min}B_{1}\times F\otimes_{min}B_{2}\rightarrow B(K)\otimes_{min}B_{1}\otimes_{min}B_{2}$ taking $(e\otimes b_{1},f\otimes b_{2})$ to $u(e,f)\otimes b_{1}\otimes b_{2}$. In this case we define $\|u\|_{jcb}=\sup_{B_{1},B_{2}}\|(u)_{B_{1},B_{2}}\|$. Is it true that $\|u\|_{jcb}\leq\|u\|_{cb}$?