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Linear preservers on upper triangular operator matrix algebras
Cui, JL; Hou, JC; Li, BR
2001-10-15
Source PublicationLINEAR ALGEBRA AND ITS APPLICATIONS
ISSN0024-3795
Volume336Pages:29-50
AbstractIn 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.
Keywordupper triangular matrix algebras rank preserving maps automorphisms Jordan isomorphisms
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000171354000004
PublisherELSEVIER SCIENCE INC
Citation statistics
Cited Times:11[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/16346
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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