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

• 论文 • 上一篇    下一篇

FREE FISHER INFORMATION AND AMALGAMATED FREENESS

孟彬, 郭懋正, 曹小红   

  1. LMAM, School of Mathematical Science, Peking University, Beijing 100871, P.R.China
  • 收稿日期:2003-06-15 修回日期:2004-06-15 出版日期:2004-10-18 发布日期:2004-10-18
  • 通讯作者: GUO Mao-zheng,Professor,Tel:+86-10-62752163;E-mail:maguo@pku.edu.cn E-mail:maguo@pku.edu.cn

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

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.

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.

中图分类号: 

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals