Complete positivity of entropy and non-Bernoullicity for transformation groups
Golodets, Valentin ; Sinel'shchikov, Sergey
Colloquium Mathematicae, Tome 84/85 (2000), p. 421-429 / Harvested from The Polish Digital Mathematics Library

The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:210823
@article{bwmeta1.element.bwnjournal-article-cmv84i2p421bwm,
     author = {Valentin Golodets and Sergey Sinel'shchikov},
     title = {Complete positivity of entropy and non-Bernoullicity for transformation groups},
     journal = {Colloquium Mathematicae},
     volume = {84/85},
     year = {2000},
     pages = {421-429},
     zbl = {0972.37006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv84i2p421bwm}
}
Golodets, Valentin; Sinel'shchikov, Sergey. Complete positivity of entropy and non-Bernoullicity for transformation groups. Colloquium Mathematicae, Tome 84/85 (2000) pp. 421-429. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv84i2p421bwm/

[000] [1] C J. P. Conze, Entropie d'un groupe abélien de transformations, Z. Wahrsch. Verw. Gebiete 25 (1972), 11-30. | Zbl 0261.28015

[001] [2] E. Glasner, J.-P. Thouvenot and B. Weiss, Entropy theory without past, preprint ESI-612. | Zbl 0965.37009

[002] [3] V. Golodets and S. Sinel'shchikov, On the entropy theory of finitely generated nilpotent group actions, preprint.

[003] [4] B. Kamiński, The theory of invariant partitions for d-actions, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 349-362. | Zbl 0479.28016

[004] [5] D. Ornstein and P. C. Shields, An uncountable family of K-automorphisms, Adv. Math. 10 (1973), 63-88. | Zbl 0251.28004

[005] [6] D. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Anal. Math. 48 (1987), 1-141. | Zbl 0637.28015

[006] [7] V. A. Rokhlin and Ya. G. Sinai, Construction and properties of invariant meas- urable partitions, Dokl. Akad. Nauk SSSR 141 (1961), 1038-1041 (in Russian).

[007] [8] D. J. Rudolph and B. Weiss, Entropy and mixing for amenable group actions, preprint. | Zbl 0957.37003