The Characterization of Generalized Jordan Centralizers on Triangular Algebras

Abstract

In this paper, it is shown that if T=Tri(A,M,B) is a triangular algebra and ϕ is an additive operator on T such that (m+n+k+l)ϕ(T2)-(mϕ(T)T+nTϕ(T)+kϕ(I)T2+lT2ϕ(I))∈FI for any T∈T, then ϕ is a centralizer. It follows that an (m,n)- Jordan centralizer on a triangular algebra is a centralizer.

Characterization of Jordan centralizers and Jordan two-sided centralizers on triangular rings without assuming unity

“…So far, many mathematicians have investigated Jordan centralizers on triangular rings (or algebras) with unity, see, e.g. [4,8,10,16,17,18], and the references therein. In the present paper, we shall initiate the study of Jordan centralizers, Jordan two-sided centralizers and some related mappings on triangular rings without assuming unity.…”