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  • CHARACTERIZATIONS OF JORDAN DERIVATIONS ON STRONGLY DOUBLE TRIANGLE SUBSPACE LATTICE ALGEBRAS

  • Part of
  • YUN-HE CHEN, JIAN-KUI LI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 84 / Issue 2 / October 2011
    Published online by Cambridge University Press:
    21 July 2011, pp. 300-309
    Print publication:
    October 2011
    • Article
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  • Let 𝒟 be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space X and let δ:Alg 𝒟→Alg 𝒟 be a linear mapping. We show that δ is Jordan derivable at zero, that is, δ(AB+BA)=δ(A)B+Aδ(B)+δ(B)A+Bδ(A) whenever AB+BA=0 if and only if δ has the form δ(A)=τ(A)+λA for some derivation τ and some scalar λ. We also show that if the dimension of X is greater than 2, then δ satisfies δ(AB+BA)=δ(A)B+Aδ(B)+δ(B)A+Bδ(A) whenever AB=0 if and only if δ is a derivation.