Processes disjoint from weak mixing

Source abstract

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