摘要
设A和B是含单位元的C~*代数,s∈A和t∈B是可逆自伴元,对任意的x∈A及z∈B,定义x^+=s^(-1)x~*s,z^+=t^(-1)z~*t。假定A是实秩零的并且Φ:A→B是有界线性满射。证明了对任意的 都成立的充要条件是Φ(1)可逆,Φ(1)^+Φ(1)=Φ(1)Φ(1)^+∈Z(B)(B的中心),并且存在从A到B上的满+同态Ψ,使得对所有的x∈A都有Φ(x)=Φ(1)Ψ(x)成立。对于一般C~*代数上保正交性的线性映射Φ,在假定Φ(1)可逆的条件下,也得到类似的结果。
Let A and B be unital C~*-algebras, s ∈A and t ∈ B be invertible self-adjoint elements. For every x ∈ A and z ∈B, define x^+=s^(-1)x~*s and z^+=t^(-1)z~*t. Assume that A is of real rank zero and φ: A→B is a bounded linear surjection. This paper shows that, x^+y=0 φ(x)^+φ(y)=0 and xy^+=0 φ(x)φ(y)^+=0 for any x, y ∈ A, if and only if φ(1) is invertible, φ(1)^+φ(1)=φ(1)φ(1)^+ ∈(B) (the center of B) and there exists a surjective +-homomorphism ψ(i.e., ψ is a homomorphism and ψ(x^+)=ψ(x)^+, x ∈A) from A onto B such that φ(x)=φ(1)ψ(x) for all x ∈A. For general C~*-algebra cases, a similar result is obtained for orthogonality preservers under an additional assumption that φ(1) is invertible.
出处
《数学年刊（A辑）》
CSCD
北大核心
2004年第4期437-444,共8页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10071046)
山西省自然科学基金(No.981009)
山西省青年科学基金
中国博士后科学基金
关键词
C^＊代数
不定正交性
同构
C~*-algebras, Indefinite orthogonality, Isomorphisms
