| 自由Fisher信息量与合并自由 |
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| 引用本文： | 孟彬,郭懋正,曹小红.自由Fisher信息量与合并自由[J].应用数学和力学,2004,25(10):1007-1013. |
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| 作者姓名： | 孟彬 郭懋正 曹小红 |
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| 作者单位： | 北京大学 数学科学学院 数学与应用数学实验室,北京 100871 |
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| 摘 要： | 在算子值非交换概率空间中引入算子值自由Fisher信息量的概念，这一定义是对D.Voiculescu在有迹的von Neumann代数上定义的自由Fisher信息量的推广．证明了算子值自由Fisher信息量与合并自由性是密切相关的，即证明了若干个算子值随机变量的自由Fisher信息量的可加性等价于这些随机变量的合并自由性．并且也类似地得到了Cramer-Rao不等式．
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| 关 键 词： | Hilbert C*-模 算子值随机变量 自由Fisher信息量 |
| 文章编号： | 1000-0887(2004)10-1007-07 |
| 收稿时间： | 2003-06-15 |
| 修稿时间： | 2003年6月15日 |
Free Fisher Information and Amalgamated Freeness |
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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. |
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| Authors: | MENG Bin GUO Mao-zheng CAO Xiao-hong |
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| Institution: | LMAM, School of Mathematical Science, Peking University, Beijing 100871, P. R. China |
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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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| Keywords: | Hilbert C~*-module operator-valued random variable free Fisher information |
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