Local and 2-Local Lie Derivations of Operator Algebras on Banach Spaces |
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Authors: | Lin Chen Fangyan Lu Ting Wang |
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Affiliation: | 1. Department of Mathematics, Soochow Univrsity, Suzhou, 215006, People’s Republic of China 2. Department of Mathematics and Computer Science, Anshun Univrsity, Anshun, 561000, People’s Republic of China 3. Department of Mathematics, Nanyang Normal Univrsity, Nanyang, 473000, People’s Republic of China
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Abstract: | Let X be a Banach space of dimension > 2. We show that every local Lie derivation of B(X) is a Lie derivation, and that a map of B(X) is a 2-local Lie derivation if and only if it has the form ${A mapsto AT - TA + psi(A)}$ A ? A T - T A + ψ ( A ) , where ${T in B(X)}$ T ∈ B ( X ) and ψ is a homogeneous map from B(X) into ${mathbb{F}I}$ F I satisfying ${psi(A + B) = psi(A)}$ ψ ( A + B ) = ψ ( A ) for ${A, B in B(X)}$ A , B ∈ B ( X ) with B being a sum of commutators. |
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