The characterization of generalized Jordan centralizers on triangular algebras (Q1624142)

Summary: In this paper, it is shown that if \(\mathcal{T} = \mathrm{Tri}(\mathcal{A}, \mathcal{M}, \mathcal{B})\) is a triangular algebra and \(\phi\) is an additive operator on \(\mathcal{T}\) such that \((m + n + k + l) \phi(T^2) -(m \phi(T) T + n T \phi(T) + k \phi(I) T^2 + l T^2 \phi(I)) \in \mathbb{F} I\) for any \(T \in \mathcal{T}\), then \(\phi\) is a centralizer. It follows that an \((m, n)\)-Jordan centralizer on a triangular algebra is a centralizer.