The spectrally bounded linear maps on operator algebras

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	The spectrally bounded linear maps on operator algebras
	Cui, J ; Hou, J
	2002
发表期刊	STUDIA MATHEMATICA
ISSN	0039-3223
卷号	150 期号:3 页码:261-271
摘要	We show that every spectrally bounded linear map Phi from a Banach algebra onto a standard operator algebra acting on a complex Banach space is square-zero preserving. This result is used to show that if Phi(2) is spectrally bounded, then Phi is a homomorphism multiplied by a nonzero complex number. As another application to the Hilbert space case, a classification theorem is obtained which states that every spectrally bounded linear bijection Phi from B(I-I) onto B(K), where H and K are infinite-dimensional complex Hilbert spaces, is either an isomorphism or an anti-isomorphism multiplied by a nonzero complex number. If P is not injective, then Phi vanishes at all compact operators.
关键词	spectral radius Jordan homomorphism isomorphism Banach algebras
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000179180800004
出版者	POLISH ACAD SCIENCES INST MATHEMATICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17319
专题	中国科学院数学与系统科学研究院
通讯作者	Cui, J
作者单位	1.Chinese Acad Sci, Inst Math, Beijing 100080, Peoples R China 2.Shandong Teachers Univ, Dept Math, Linfen 041004, Peoples R China 3.Shanxi Univ, Dept Math, Tiyuan 030000, Peoples R China
推荐引用方式 GB/T 7714	Cui, J,Hou, J. The spectrally bounded linear maps on operator algebras[J]. STUDIA MATHEMATICA,2002,150(3):261-271.
APA	Cui, J,&Hou, J.(2002).The spectrally bounded linear maps on operator algebras.STUDIA MATHEMATICA,150(3),261-271.
MLA	Cui, J,et al."The spectrally bounded linear maps on operator algebras".STUDIA MATHEMATICA 150.3(2002):261-271.