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Jordan *-derivations on \(C^*\)-algebras and \(JC^*\)-algebras. (English) Zbl 1243.46046

Summary: We investigate Jordan *-derivations on \(C^*\)-algebras and Jordan *-derivations on \(JC^*\)-algebras associated with the following functional inequality \(\| f(x)+f(y)+kf(z)\| \leq \| kf((x+y)/k+z)\| \) for some integer \(k\) greater than 1. We moreover prove the generalized Hyers-Ulam stability of Jordan *-derivations on \(C^*\)-algebras and of Jordan *-derivations on \(JC^*\)-algebras associated with the following functional equation \(f((x+y)/k+z)=(f(x)+f(y))/k+f(z)\) for some integer \(k\) greater than 1.

MSC:

46L05 General theory of \(C^*\)-algebras
46L70 Nonassociative selfadjoint operator algebras
39B82 Stability, separation, extension, and related topics for functional equations
47B47 Commutators, derivations, elementary operators, etc.
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