In Rota's paper (An Alternierende Verfahren for General Positive Operators), Theorem 2 says that: Let $P$ be a doubly stochastic operator which is selfadjoint in $L^2 (S, \Sigma, \mu)$. Then there is a dilation of the sequence of operators $P^{2n}$ into a martingale $E_n$.
My question is, what does he mean by a dilation? Is he referring to the definition of dilation: $Q$ is a dilation of $T$ in $T^n = EQ^n D$ where $T:V\to V$, $Q:W\to W$ and $D: V\to W$?
