Generalized Jordan centralizer mapping on completely distributive commutative subspace lattice algebras
MA Fei1*, ZHANG Jianhua2, WANG Baoshe1
(1 College of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, Shaanxi, China;2 School of Mathematics and Information Science, Shaanxi Normal University,Xi′an 710119, Shaanxi, China)
Abstract:
Based on a completely distributive commutative subspace lattice L on a Hilbert H, the centralizer mapping on the completely distributive commutative subspace lattice algebras Alg L is discussed.Let Φ:Alg L→Alg L be an additive mapping. According to the structural properties and algebraic decomposition on the completely distributive commutative subspace lattice algebras, it is proved that if there are some positive integer numbers m,n,r≥1, such that A∈Alg L, (m+n)Φ(Ar+1)-(mΦ(A)Ar+nArΦ(A))∈Z(Alg L), then there exists some λ∈Z(Alg L), which satisfies A∈Alg L,Φ(A)=λA.
KeyWords:
centralizer mapping; additive map; completely distributive commutative subspace lattice algebra
