Characterizations of Lie Derivations on the Algebra of Operators in Hilbert C*-modules
Let A be a commutative unital C*-algebra with the unit element e and M be a full Hilbert A-module.Denote by EndA(M)the algebra of all bounded A-linear mappings on M and by M'the set of all bounded A-linear mappings from M into A.In this paper,we prove that if there exist x0 in M and f0 in M'such that f0(x0)=e,then every A-linear Lie derivation δ on EndA(M)is standard.That is,δcan be decomposed into d+τ,where d is a A-linear derivation,and τ is a A-linear mapping of central value such that τ(AB)=τ(BA)for any A,B ∈ EndA(M).
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