An algebraic invariant for Jordan automorphisms on B(H): The set of idempotents
Let H be an infinite dimensional complex Hilbert space. Denote by B(H)the algebra of all bounded linear operators on H, and by I(H) the set of all idempotents in B(H). Suppose that φ is a surjective map from B(H) onto itself. If for everyλ∈ {-1, 1, 2, 3, 1/2, 1/3} and A, B ∈ B(H), A - λB ∈ I(H) (→)φ(A) - λφ(B) ∈ I(H), then φis a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that φ(A) = TAT-1 for all A ∈ B(H), or φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A - iB ∈ I(H) (→)φ(A) - iφ(B) ∈ I(H), here i is the imaginary unit, then φ is either an automorphism or an anti-automorphism.
作 者： CUI Jianlian HOU Jinchuan 作者单位： CUI Jianlian(Department of Mathematical Science,Tsinghua University,Beijing 100084,China)HOU Jinchuan(Department of Applied Mathematics,Taiyuan University of Technology,Taiyuan 030024,China;Department of Mathematics,Shanxi Teachers University,Linfen 041004,China)
刊 名： 中国科学A辑（英文版） SCI 英文刊名： SCIENCE IN CHINA SERIES A (MATHEMATICS) 年，卷(期)： 2005 48(12) 分类号： O1 关键词： Hilbert space operators Jordan automorphisms idempotents