Processes disjoint from weak mixing

Abstract:

We show that the family ${\mathcal {W}^ \bot }$ of ergodic measure preserving transformations which are disjoint from every weakly mixing m.p.t. properly contains the family $\mathcal {D}$ of distal ergodic m.p.t. In the topological case we show that $\mathcal {P}\mathcal {I}$, the family of proximally isometric flows is properly contained in the family $\mathcal {M}({\mathcal {W}^ \bot })$ of multipliers for ${\mathcal {W}^ \bot }$.