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| A Characterization of Generalized Derivations of JSL Algebras |
| Lin CHEN1, Fang Yan LU1,2 |
1 Department of Mathematics, Soochow University, Suzhou 215006, P. R. China;
2 Department of Mathematics, Anshun University, Anshun 561000, P. R. China |
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Abstract Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. 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 ∈ AlgL 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.
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Received: 26 April 2016
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| Fund: Supported by the National Natural Science Foundation of China (Grant No. 11571247); the first author is supported by the union program of department of science technology in Guizhou province, Anshun government and Anshun university (Grant No. 201304) |
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2017, Vol. 33 
