Characterizations of Lie derivations of B(X)

By Fangyan Lu, W. Jing. 2010

60 citations recorded by the source corpus.

Abstract Let X be a Banach space of dimension greater than 2. We prove that if δ : B ( X ) → B ( X ) is a linear map satisfying δ ( [ A , B ] ) = [ δ ( A ) , B ] + [ A , δ ( B ) ] for any A , B ∈ B ( X ) with AB = 0 (resp. AB = P , where P is a fixed nontrivial idempotent), then δ = d + τ , where d is a derivation of B ( X ) and τ : B ( X ) → C I is a linear map vanishing at commutators [ A , B ] with AB = 0 (resp. AB = P ).

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/01868f9b315038c900a7473658a3010951594a33

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In Algebra and Number Theory

1. Yiqiu Du
2. Yu Wang
3. Xiaomin Tang

In Geometry and Topology

1. Yiqiu Du
2. Yu Wang
3. Xiaomin Tang

Citations in the corpus

• Lie derivations of generalized matrix algebras (2012, background): “Lie derivations have been discussed by many authors (see [1,2,4,6,7,10,12]).”