Structure and related applications of ternary derivations on J-subspace lattice algebras
Document Type
Article
Publication Date
2026
Abstract
Let L be a J-subspace lattice on Banach space X and AlgL be the associated J-subspace lattice algebra. A ternary derivation on AlgL is defined as a triple of linear mappings (γ,δ,τ):AlgL→AlgL that satisfies the condition γ(AB)=δ(A)B+Aτ(B) for all A,B∈AlgL. We establish that for given linear maps δ,τ on AlgL, there exists a unique linear map γ on AlgL defined by γ(A)=RA+AS for some R,S∈L(X) such that (γ,δ,τ) forms a ternary derivation on AlgL if and only if δ,τ satisfy δ(A)B+Aτ(B)=0 for any A,B∈AlgL with AB=0. As applications of this result, we provide a comprehensive characterization of linear mappings δ and τ. Additionally, we investigate linear mappings that are derivable at zero, (left/right) centralizers, (left/right) ideal-preserving mappings, and local (generalized) derivations within JSL algebras. These findings are applicable to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras in Banach spaces. © Università degli Studi di Napoli "Federico II" 2025.
Recommended Citation
Fadaee, Behrooz; Ghahramani, Hoger; and Jing, Wu, "Structure and related applications of ternary derivations on J-subspace lattice algebras" (2026). College of Health, Science, and Technology. 1202.
https://digitalcommons.uncfsu.edu/college_health_science_technology/1202