Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (10): 1100-1106.

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FREE FISHER INFORMATION AND AMALGAMATED FREENESS

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

  1. LMAM, School of Mathematical Science, Peking University, Beijing 100871, P.R.China
  • Received:2003-06-15 Revised:2004-06-15 Online:2004-10-18 Published:2004-10-18

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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