On (m,n,l)-Jordan Centralizers of Some Algebras

Abstract

Let A be a unital algebra over a number field K. A linear mapping δ from A into itself is called a weak (m,n,l )-Jordan centralizer if (m + n + l)δ(A 2 ) − mδ(A)A − nAδ(A) − lAδ(I)A ∈ KI for every A ∈ A, where m ≥ 0, n ≥ 0, l ≥ 0 are fixed integers with m+n+l = 0. In this paper, we study weak (m,n,l )-Jordan centralizer on generalized matrix algebras and some reflexive algebras algL, where L is a CSL or satisfies ∨{L : L ∈ J (L)} = X or ∧{L − : L ∈ J (L)} = (0), and prove that each weak (m,n,l )-Jordan centralizer of these algebras is a centralizer when m + l ≥ 1 and n + l ≥ 1.