Approximation of homomorphisms and derivations on Lie \(C^\ast\)-algebras via fixed point method. (English) Zbl 1285.39010
Summary: Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in \(C^\ast\)-algebras and Lie \(C^\ast\)-algebras and of derivations on \(C^\ast\)-algebras and Lie \(C^\ast\)-algebras for an \(m\)-variable additive functional equation.
MSC:
39B82 | Stability, separation, extension, and related topics for functional equations |
39B52 | Functional equations for functions with more general domains and/or ranges |
46L05 | General theory of \(C^*\)-algebras |
46L57 | Derivations, dissipations and positive semigroups in \(C^*\)-algebras |
Keywords:
additive functional equation; homomorphism in \(C^\ast\)-algebras and Lie \(C^\ast\)-algebras; generalized Hyers-Ulam stability; derivation on \(C^\ast\)-algebras and Lie \(C^\ast\)-algebras; fixed point methodsReferences:
[1] | doi:10.1080/10236190500273226 · Zbl 1085.39027 · doi:10.1080/10236190500273226 |
[2] | doi:10.1016/j.jmaa.2008.03.039 · Zbl 1228.39025 · doi:10.1016/j.jmaa.2008.03.039 |
[3] | doi:10.1007/s10474-011-0116-0 · Zbl 1299.39019 · doi:10.1007/s10474-011-0116-0 |
[4] | doi:10.1016/j.jmaa.2003.10.051 · Zbl 1051.46052 · doi:10.1016/j.jmaa.2003.10.051 |
[5] | doi:10.1007/s00574-005-0029-z · Zbl 1091.39007 · doi:10.1007/s00574-005-0029-z |
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