TY - JOUR
T1 - On the K property for Maharam extensions of Bernoulli shifts and a question of Krengel
AU - Kosloff, Zemer
N1 - Publisher Copyright:
© 2014, Hebrew University Magnes Press.
PY - 2014/1/1
Y1 - 2014/1/1
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=84886745124&partnerID=8YFLogxK
U2 - 10.1007/s11856-013-0069-9
DO - 10.1007/s11856-013-0069-9
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AN - SCOPUS:84886745124
SN - 0021-2172
VL - 199
SP - 485
EP - 506
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -