Invariant subspaces of super left-commutants.

For a positive operator $Q$ on a Banach lattice, one defines $langle Q]={Tgeq 0:~TQleq QT}$ and $[Qrangle ={Tgeq 0: TQgeq QT}$. There have been several recent results asserting that, under certain assumptions on $Q$, $[Qrangle $ has a common invariant subspace. In this paper, we use the technique of minimal vectors to establish similar results for $langle Q]$. [ABSTRACT FROM AUTHOR]