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

Zemer Kosloff

doi:10.1007/s11856-013-0069-9

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 III_λ 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.

Original language	English
Pages (from-to)	485-506
Number of pages	22
Journal	Israel Journal of Mathematics
Volume	199
Issue number	1
DOIs	https://doi.org/10.1007/s11856-013-0069-9
State	Published - 1 Jan 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-013-0069-9

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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{\textquoteright}s and Weiss{\textquoteright}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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AB - 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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DO - 10.1007/s11856-013-0069-9

M3 - مقالة

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VL - 199

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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

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

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