Acta Mathematica Sinica, English Series

, Volume 33, Issue 4, pp 495–500 | Cite as

A characterization of generalized derivations of JSL algebras

Article

Abstract

Let Alg ℒ be a J -subspace lattice algebra on a Banach space X and M be an operator in Alg ℒ. We prove that if δ: Alg ℒ → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B) for all A,B ∈ Alg ℒ with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.

Keywords

Generalized derivation derivation derivable mapping 

MR(2010) Subject Classification

47B47 47B49 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsSoochow UniversitySuzhouP. R. China
  2. 2.Department of MathematicsAnshun UniversityAnshunP. R. China

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