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Comment on “Stability of \((\alpha,\beta,\gamma)\)-derivations on Lie \(C^*\)-algebras” by M. Eshaghi Gordji and N. Ghobadipour. (English) Zbl 1282.39034
The authors comment on the paper [ibid. 7, No. 7, 1093–1102 (2010; Zbl 1217.39034)] mentioned in the title. Therein M. Eshaghi Gordji and N. Ghobadipour proved the Hyers–Ulam stability of \((\alpha, \beta, \gamma)\)-derivations on Lie \(C^*\)-algebras associated with the functional equation \[ f\left(\frac{x_2-x_1}{3}\right) + f\left(\frac{x_1-3x_3}{3}\right)+f\left(\frac{3x_1 +3x_3-x_2}{3}\right)=f(x_1). \] In the paper under review, the authors prove that under the conditions given in the main theorems of the paper quoted in the title, the related mappings are identically zero. In this paper, the authors give the correct version of the statement.
MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
46L57 Derivations, dissipations and positive semigroups in \(C^*\)-algebras
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