  Let $\mathcal{M}\subseteq\mathcal{B}\left( \mathcal{H}\right) $ be a
countable decomposable properly infinite von Neumann algebra with a faithful
normal semifinite tracial weight $\tau$ where $\mathcal{B}\left(
\mathcal{H}\right) $ is the set of all bounded linear operators on Hilbert
space $\mathcal{H}.$ The main purpose of this article is to introduce
generalized weak wave operators $\widetilde{W}_{\pm}$, generalized weak abelian
wave operators $\widetilde{\mathfrak{U}}_{\pm}$ and generalized stationary wave
operators $\mathcal{U}_{\pm}$ in $\mathcal{M}$ and then to explore the relation
among $\widetilde{W}_{\pm},$ $\widetilde{\mathfrak{U}% }_{\pm}$,
$\mathcal{U}_{\pm}$ and generalized wave operators $W_{\pm}.$
