Linear maps on von Neumann algebras preserving zero products or tr-rank

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	Linear maps on von Neumann algebras preserving zero products or tr-rank
	Cui, JL ; Hou, JC
	2002-02-01
发表期刊	BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
ISSN	0004-9727
卷号	65 期号:1 页码:79-91
摘要	In this paper, we give some characterisations of homomorphisms on von Neumann algebras by linear preservers. We prove that a bounded linear surjective map from a von Neumann algebra onto another is zero-product preserving if and only if it is a homomorphism multiplied by an invertible element in the centre of the image algebra. By introducing the notion of tr-rank of the elements in finite von Neumann algebras, we show that a unital linear map from a linear subspace M of a finite von Neumann algebra R into R can be extended to an algebraic homomorphism from the subalgebra generated by M into R; and a unital self-adjoint linear map from a finite von Neumann algebra onto itself is completely tr-rank preserving if and only if it is a spatial *-automorphism.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000174530100009
出版者	AUSTRALIAN MATHEMATICS PUBL ASSOC INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17772
专题	中国科学院数学与系统科学研究院
作者单位	1.Chinese Acad Sci, Math Inst, Beijing 100080, Peoples R China 2.Taiyuan Univ Technol, Dept Math Appl, Taiyuan 030024, Peoples R China 3.Shanxi Teachers Univ, Dept Math, Linfen 041004, Peoples R China
推荐引用方式 GB/T 7714	Cui, JL,Hou, JC. Linear maps on von Neumann algebras preserving zero products or tr-rank[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY,2002,65(1):79-91.
APA	Cui, JL,&Hou, JC.(2002).Linear maps on von Neumann algebras preserving zero products or tr-rank.BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY,65(1),79-91.
MLA	Cui, JL,et al."Linear maps on von Neumann algebras preserving zero products or tr-rank".BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 65.1(2002):79-91.