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On the K property for Maharam extensions of Bernoulli shifts and a question of Krengel

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Abstract

We show that the Maharam extension of a type III, conservative and nonsingular K Bernoulli is a K-transformation. This together with the fact that the Maharam extension of a conservative transformation is conservative gives a negative answer to Krengel’s and Weiss’s questions about existence of a type II∞ or type IIIλ with λ ≠ 1 Bernoulli shift. A conservative non-singular K, in the sense of Silva and Thieullen, Bernoulli shift is either of type II1 or of type III1.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Zemer Kosloff

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  1. Zemer Kosloff
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Correspondence to Zemer Kosloff.

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This research was was supported by The Israel Science Foundation grant No. 1114/08.

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Kosloff, Z. On the K property for Maharam extensions of Bernoulli shifts and a question of Krengel. Isr. J. Math. 199, 485–506 (2014). https://doi.org/10.1007/s11856-013-0069-9

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  • DOI: https://doi.org/10.1007/s11856-013-0069-9

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