Free Fisher Information and Amalgamated Freeness

MENG Bin; GUO Mao-zheng; CAO Xiao-hong

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MENG Bin, GUO Mao-zheng, CAO Xiao-hong. Free Fisher Information and Amalgamated Freeness[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1007-1013.

Citation:

MENG Bin, GUO Mao-zheng, CAO Xiao-hong. Free Fisher Information and Amalgamated Freeness[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1007-1013.

Citation:

MENG Bin, GUO Mao-zheng, CAO Xiao-hong. Free Fisher Information and Amalgamated Freeness[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1007-1013.

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Free Fisher Information and Amalgamated Freeness

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

Received Date: 2003-06-15
Rev Recd Date: 2004-06-15
Publish Date: 2004-10-15

Abstract

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-Raoinequality in operator-valued settings is also obtained.
- Hilbert C^*-module,
- operator-valued random variable,
- free Fisher information

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References(9)

References

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