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Ternary homomorphisms between unital ternary \(C^*\)-algebras. (English) Zbl 1324.46067

Summary: Let \(A,B\) be two unital ternary \(C^*\)-algebras. We prove that every almost unital almost linear mapping \(h:A\to B\) which satisfies \(h([{}_3 n_u {}_3 n_{vy}]_A)=[h(_3 n_u)h({}_3 n_v)h(y)]_B\) for all \(u, v\in U(A)\), all \(y\in A\), and all \(n=0,1,2,\dots\), is a ternary homomorphism. Also, for a unital ternary \(C^*\)-algebra \(A\) of real rank zero, every almost unital almost linear continuous mapping \(h:A\to B\) is a ternary homomorphism when \(h([{}_3 n_u {}_3 n_{vy}]_A)=[h({}_3 n_u)h({}_3 n_v)h(y)]_B\) holds for all \(u, v\in I_1(A_{sa})\), all \(y\in A\), and all \(n=0,1,2,\dots\). Furthermore, we investigate the Hyers-Ulam-Rassias stability of ternary homomorphisms between unital ternary \(C^*\)-algebras.

MSC:

46L05 General theory of \(C^*\)-algebras
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