Abstract:
Based on a lattice L of a Banach space X with X_≠X,the centralizers on the reflexive algebras AlgL are discussed.Let Φ:AlgL→AlgL be an additive mapping and using the structural properties and algebraic decomposition on the reflexive algebra,it is proved that if there are some positive integer numbers m,n,r≥1,such that A∈A,(m+n)Φ(Ar+1)=mΦ(A)Ar+nArΦ(A) or Φ(Am+n+1)=AmΦ(A)An,then there exists some λ∈F,which satisfies A∈AlgL,Φ(A)=λA.In addition,some equivalent forms of centralizer on the reflexive algebras Alg L are obtained.
