On the class of multipliers for W

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Abstract

Let W┴ be the class of all ergodic measure-preserving transformations (systems), which are disjoint from every weakly mixing system. Let M(W┴) be the class of multipliers for W┴; i.e. the class of all systems (X, μ, T) in W┴ such that for every system (Y, ν, T) ∊ W┴ and every ergodic joining λ of X and Y, the system (X × Y, λ, T × T) is also in W┴. Well known results on disjointness show that the class D of ergodic distal systems, is a subclass of M(W┴). Thus one has D ∊ M(W┴) ∊ W┴. Glasner and Weiss have shown that D ≠ W┴. The purpose of this paper is to also show that D ≠ M(W┴). The question whether M(W┴) = W┴ remains open.

Original languageEnglish
Pages (from-to)129-140
Number of pages12
JournalErgodic Theory and Dynamical Systems
Volume14
Issue number1
DOIs
StatePublished - Mar 1994

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