Abstract:

 Let A be a a standard operator algebra on Banach space X with unit I, and φ:A→B(X) is an additive mapping. In this paper, we prove that if there is some positive integer number m,n,r satisfies (m+n)φ(Ar+1)-(mφ(A)Ar+nArφ(A))∈FI, for all A∈A, then there exists some λ∈F, such that φ(A)=λA for all A∈A.

Key words: additive map; centralizers; standard operator algebras