Cross-covariance operator ($C_{YX}$)

For centered Hilbert-space random variables $X$ and $Y$, the cross-covariance operator is $C_{YX}h=\mathbb{E}[⟨X,h⟩Y]$. In the functional linear model $Y=BX+\epsilon$ with independent centered error, $C_{YX}=B{C}_X$.