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Free fisher information and amalgamated freeness

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Abstract

The notion of operator-valued free Fisher information was introduced. It is a generalization of free Fisher information which was defined by D. Voiculescu on tracial von Neumann algebras. It is proved that the operator-valued free Fisher information is closely related to amalgamated freeness, i. e., the operator-valued free Fisher information of some random variables is additive if and only if these random variables are a free family with amalgamation over a subalgebra. Cramer-Rao inequality in operator-valued settings is also obtained.

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Authors and Affiliations

  1. LMAM, School of Mathematical Science, Peking University, 100871, Beijing, P.R. China

    Meng Bin Doctor, Guo Mao-zheng Professor & Cao Xiao-hong

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  1. Meng Bin Doctor
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  2. Guo Mao-zheng Professor
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  3. Cao Xiao-hong
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Correspondence to Guo Mao-zheng Professor.

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Contributed by Guo Mao-zheng

Biographies: Meng Bin (1976≈)

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Bin, M., Mao-zheng, G. & Xiao-hong, C. Free fisher information and amalgamated freeness. Appl Math Mech 25, 1100–1106 (2004). https://doi.org/10.1007/BF02439862

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  • DOI: https://doi.org/10.1007/BF02439862

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2000 Mathematics Subject Classification

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