Freeness and matrix decompositions

doi:10.1007/s11425-011-4323-5

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	Freeness and matrix decompositions
	Ge Liming1,2 ; Shen Junhao 1
	2011-11-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	54 期号:11 页码:2309-2327
摘要	If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra (with respect to a normal trace), then, up to the conjugation by a diagonal unitary element, all entries of the semicircular element are uniquely determined in the sense of (joint) distribution. Suppose a selfadjoint element is free with the diagonal subalgebra. Then, in the matrix decomposition of the selfadjoint element, any two entries cannot be free with each other unless the selfadjoint element is semicircular. We also define a "matricial distance" between two elements and show that such distance for two free semicircular elements in a finite von Neumann algebra is nonzero and independent of the properties of the von Neumann algebra.
关键词	von Neumann algebra factor semicircular element joint distribution
DOI	10.1007/s11425-011-4323-5
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000296637700004
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12611
专题	数学所
通讯作者	Shen Junhao
作者单位	1.Univ New Hampshire, Dept Math, Durham, NH 03824 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Ge Liming,Shen Junhao. Freeness and matrix decompositions[J]. SCIENCE CHINA-MATHEMATICS,2011,54(11):2309-2327.
APA	Ge Liming,&Shen Junhao.(2011).Freeness and matrix decompositions.SCIENCE CHINA-MATHEMATICS,54(11),2309-2327.
MLA	Ge Liming,et al."Freeness and matrix decompositions".SCIENCE CHINA-MATHEMATICS 54.11(2011):2309-2327.