. Let $E_0^{\rho, u}$ and $E_0^{\sigma, v}$ be the canonical conditional expectations from $C$ and $D$ onto $A$ defined by $$E_0^{\rho, u}(a\rtimes_{\rho, u}h)=\tau(h)a , \quad E_0^{\sigma, v}(a\rtimes_{\sigma, v}h)=\tau(h)a$$ for any $a\in A$, $h\in H$