FREE FISHER INFORMATION AND AMALGAMATED FREENESS  

作　　者：孟彬 郭懋正 曹小红 

机构地区：[1]LMAM School of Mathematical Science Peking University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2004年第10期1100-1106,共7页应用数学和力学（英文版）

摘　　要：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.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.

关 键 词：Hilbert C~*-module operator-valued random variable free Fisher information 

分 类 号：O177.1[理学—数学]