I am reading King's paper "The commutant is the weak closure of the powers, for rank-1 transformation" and I am not able to show that:
(0.1) "If the $T_i$ are invertible measure preserving transformations on Lebesgue probability space, commuting with each other and converging weakly to $S$ then $S$ is invertible and $T_i^{-1}\rightarrow S^{-1}$ weakly."
Does anybody have any ideas how the proof my go? Btw, the result is not true if $T_i$ are not assumed to be commutative which I also don't see why.