Additive maps derivable at some points on J-subspace lattice algebras
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Abstract Let L be a J -subspace lattice on a real or complex Banach space dim X with X > 2 and Alg L be the associated J -subspace lattice algebra. Let δ : Alg L → Alg L be an additive map. It is shown that, if δ is derivable at zero point, i.e., δ ( AB ) = δ ( A ) B + A δ ( B ) whenever AB = 0, then δ ( A ) = τ ( A ) + λ A , ∀ A , where τ is an additive derivation and λ is a scalar; if δ is generalized derivable at zero point, i.e., δ ( AB ) = δ ( A ) B + A δ ( B ) - A δ ( I ) B whenever AB = 0, then δ is a generalized derivation. It is also shown that, if X is complex, then every linear map derivable at unit operator on Alg L is a derivation.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/440366db8dce262e5844b2f0e79040d893c60b07