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On the class of multipliers for W

Published online by Cambridge University Press:  19 September 2008

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

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 DW. The purpose of this paper is to also show that D ≠ M(W). The question whether M(W) = W⊥ remains open.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1994

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References

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