Acta Mathematica Sinica, English Series

, Volume 33, Issue 4, pp 495–500

A characterization of generalized derivations of JSL algebras

Article

DOI: 10.1007/s10114-016-6235-3

Cite this article as:
Chen, L. & Lu, F.Y. Acta. Math. Sin.-English Ser. (2017) 33: 495. doi:10.1007/s10114-016-6235-3
  • 35 Downloads

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 

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