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 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
