Consider two Hilbert spaces $H$ and $K$ and a bounded operator $T$ on $H\oplus K$. I know that there is a theorem which says the following:
$T\ge 0$ (in the operator sense) if and only if $T$ can be represented as $$T=\begin{pmatrix} A & \sqrt{A} V \sqrt{D} \\ \sqrt{D} V^* \sqrt{A} & D \end{pmatrix}$$ for positive $A,D$ and $\|V\|\le 1$.
I am interested in the proof of this theorem (more precisely, in the exact structure of the $V$ in question). I would be very grateful for a reference to this result. I've heard it should be in Foias, Frazho, "The Commutant Lifting Approach to Interpolation Problems", but I cannot find it there...