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Weakly isomorphic transformations that are not isomorphic. (English) Zbl 0628.60015
A new method for construction of transformations T: (X$${}_ i,{\mathcal B}_ i,\mu _ i)$$, $$i=1,2$$, that are factors of each other but that are not measure-theoretically isomorphic is provided. This method uses ergodic product cocycles of the form $$\phi \circ S^{i_ 1}\times \phi \circ S^{i_ 2}\times...$$, where $$\phi$$ : $$X\to Z_ 2$$ is a cocycle, S belongs to the centralizer of T and T is an ergodic translation on a compact, monothetic group X.

##### MSC:
 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization 28D05 Measure-preserving transformations
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##### References:
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