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.
Citation: Zijie Qin, Lin Chen. Characterization of ternary derivation of strongly double triangle subspace lattice algebras[J]. AIMS Mathematics, 2023, 8(12): 29368-29381. doi: 10.3934/math.20231503
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.
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Zijie Qin, Lin Chen. Characterization of ternary derivation of strongly double triangle subspace lattice algebras[J]. AIMS Mathematics, 2023, 8(12): 29368-29381. doi: 10.3934/math.20231503
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