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	Indefinite orthogonality preserving additive maps
	Cui, JL ; Hou, J ; Park, CG
	2010-05-06 ; 2010-05-06
关键词	NUMERICAL RADIUS DISTANCE WIGNERS THEOREM RANK-ONE TRANSFORMATIONS ALGEBRAS SPACES B(H) Mathematics
中文摘要	Let H, K be real or complex complete indefinite inner product spaces of infinite dimension and let Phi : B(H) --> B(K) be an additive bijection. We show that Phi preserves indefinite orthogonality, i.e., T-dagger S = 0 double right arrow Phi(T)(dagger) Phi(S) = 0 and TSdagger = 0 double right arrow Phi(T)Phi(S)(dagger) = 0 for any T, S is an element of B(H), if and only if there exist linear or conjugate linear bounded invertible operators U : H --> K and V : K --> H, which satisfy that both (UU)-U-dagger and (VV)-V-dagger are real scalar multiples of the identity, such that Phi(T) = UTV for all T is an element of B(H), where, for R is an element of B(H, K), R-dagger stands for the conjugate of R with respect to the indefinite inner products. A similar result is also true in the finite dimensional case if Phi(I) is assumed to be invertible.
语种	英语 ; 英语
出版者	BIRKHAUSER VERLAG AG ; BASEL ; VIADUKSTRASSE 40-44, PO BOX 133, CH-4010 BASEL, SWITZERLAND
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/13954]
专题	清华大学
推荐引用方式 GB/T 7714	Cui, JL,Hou, J,Park, CG. Indefinite orthogonality preserving additive maps[J],2010, 2010.
APA	Cui, JL,Hou, J,&Park, CG.(2010).Indefinite orthogonality preserving additive maps..
MLA	Cui, JL,et al."Indefinite orthogonality preserving additive maps".(2010).

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