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Relative entropy tuples, relative u.p.e. and c.p.e. extensions

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Abstract

Relative entropy tuples both in topological and measure-theoretical settings, relative uniformly positive entropy (rel.-u.p.e.) and relative completely positive entropy (rel.-c.p.e.) are studied. It is shown that a relative topological Pinsker factor can be deduced by the smallest closed invariant equivalence relation containing the set of relative entropy pairs. A relative disjointness theorem involving relative topological entropy is proved. Moreover, it is shown that the product of finite rel.-c.p.e. extensions is also rel.-c.p.e..

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China

    Wen Huang, Xiangdong Ye & Guohua Zhang

  2. Institut de mathématiques de Luminy, 163 Avenue de Luminy, case 907, 13288, Marseille cedex 9, France

    Wen Huang

Authors
  1. Wen Huang
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  2. Xiangdong Ye
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  3. Guohua Zhang
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Additional information

The first author is partially supported by NCET, NNSF of China (no. 10401031) and CNRS-K.C.Wong Fellowship.

The second author is supported by the national key project for basic science (973).

The third author is supported by NNSF of China (no. 10401031).

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Huang, W., Ye, X. & Zhang, G. Relative entropy tuples, relative u.p.e. and c.p.e. extensions. Isr. J. Math. 158, 249–283 (2007). https://doi.org/10.1007/s11856-007-0013-y

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  • DOI: https://doi.org/10.1007/s11856-007-0013-y

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