Linear preservers on upper triangular operator matrix algebras

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	Linear preservers on upper triangular operator matrix algebras
	Cui, JL ; Hou, JC ; Li, BR
	2001-10-15
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	336 页码:29-50
摘要	In this paper, we obtain several characterizations of rank preserving linear maps and completely rank nonincreasing linear maps on upper triangular Hilbert space operator matrix algebras and apply them to get some algebraic results. We show that every automorphism of an upper triangular operator matrix algebra is inner and every weakly continuous surjective local automorphism is in fact an automorphism. A weakly continuous linear bijection on an upper triangular operator matrix algebra is idempotent preserving if and only if it is a Jordan homomorphism, and in turn, if and only if it is an automorphism or an anti-automorphism. As an application, we also obtain a result concerning the asymptotic joint-similarity of matrix tuples. (C) 2001 Elsevier Science Inc. All rights reserved.
关键词	upper triangular matrix algebras rank preserving maps automorphisms Jordan isomorphisms
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000171354000004
出版者	ELSEVIER SCIENCE 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/16346
专题	中国科学院数学与系统科学研究院
通讯作者	Cui, JL
作者单位	1.Chinese Acad Sci, Inst Math, Beijing 10080, Peoples R China 2.Shanxi Teachers Univ, Dept Math, Linfen 041004, Peoples R China 3.Chinese Acad Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Cui, JL,Hou, JC,Li, BR. Linear preservers on upper triangular operator matrix algebras[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2001,336:29-50.
APA	Cui, JL,Hou, JC,&Li, BR.(2001).Linear preservers on upper triangular operator matrix algebras.LINEAR ALGEBRA AND ITS APPLICATIONS,336,29-50.
MLA	Cui, JL,et al."Linear preservers on upper triangular operator matrix algebras".LINEAR ALGEBRA AND ITS APPLICATIONS 336(2001):29-50.