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Characterizations of Lie derivations of B(X). (English) Zbl 1188.47029
The authors study a variant of the concept of a Lie derivation in the setting of bounded linear operators on a Banach space X of dimension at least¬†3. The two results proven in this paper state that, if δ:B(X)B(X) is a linear mapping satisfying the Lie derivation property on commutators [a,b] with (i) ab=0 or (ii) ab is a fixed non-trivial idempotent¬†p, then δ is the sum of a derivation d on B(X) and a linear centre-valued mapping τ vanishing on commutators [a,b] satisfying (i) or (ii), respectively.
MSC:
47B47Commutators, derivations, elementary operators, etc.
47L10Algebras of operators on Banach spaces and other topological linear spaces
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