Characterizing centralizers and generalized derivations on triangular algebras by acting on zero product (Q353602)

In this paper, the authors show that an additive linear map on a triangular ring is centralized at zero point if and only if it is a centralizer. They also show that, for an additive linear map on a triangular ring, the following statements are equivalent: (1) It is specially generalized derivable at zero point. (2) It is generalized derivable at zero point. (3) It is a special generalized derivation. (4) It is a generalized derivation. As an application, they characterize the additive linear maps on a nest algebra over a Banach space.