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Isomorphisms between \(C^{*}\)-ternary algebras. (English) Zbl 1112.39023
Summary: We prove the Hyers-Ulam-Rassias stability of homomorphisms in \(C^*\)-ternary algebras and of derivations on \(C^*\)-ternary algebras for the following generalized Cauchy-Jensen additive mapping: \[ 2f\Biggl( \frac{\sum_{j=1}^p x_j}{2}+ \sum_{j=1}^d y_j\Biggr)= \sum_{j=1}^p f(x_j)+2 \sum_{j=1}^d f(y_j). \]
This is applied to investigate isomorphisms between \(C^*\)-ternary algebras. The concept of Hyers-Ulam-Rassias stability originated from the Rassias stability theorem that appeared in his paper: “On the stability of the linear mapping in Banach spaces” [Proc. Am. Math. Soc. 72, 297–300 (1978; Zbl 0398.47040)].

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
15A30 Algebraic systems of matrices
46L05 General theory of \(C^*\)-algebras
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