Characterization of ternary derivation of strongly double triangle subspace lattice algebras

Abstract

Let $ \mathcal{D} $ be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space. In this paper, we characterize the linear maps $ \delta, \tau $: $ {\rm{Alg}}\mathcal{D}\to {\rm{Alg}}\mathcal{D} $ satisfying $ \delta(A)B+A\tau(B) = 0 $ for any $ A, B\in {\rm{Alg}}\mathcal{D} $ with $ AB = 0 $. This result can be used to characterize linear maps derivable (centralized) at zero point and local centralizers on $ {\rm{Alg}}\mathcal{D} $, respectively.

Keywords

• ternary derivation
• derivation
• centralizer
• strongly double triangle subspace lattice