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On the class of multipliers for W⊥

Published online by Cambridge University Press:  19 September 2008

Eli Glasner
Eli Glasner
Affiliation:
School of Mathematics, Tel-Aviv University, Tel-Aviv, 69978, Israel.
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 1 , March 1994 , pp. 129 - 140
Copyright
Copyright © Cambridge University Press 1994

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