Additive functional equations and partial multipliers in \(C^*\)-algebras

Abstract

In this paper, we solve the additive functional equations

and

where s is a fixed nonzero complex number.

Furthermore, we prove the Hyers–Ulam stability of the additive functional equations (1) and (2) in complex Banach spaces. This is applied to investigate partial multipliers in Banach \(*\)-algebras, unital \(C^*\)-algebras, Lie \(C^*\)-algebras, \(JC^*\)-algebras and \(C^*\)-ternary algebras, associated with the additive functional equations (1) and (2).

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Acknowledgements

C. Park was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2017R1D1A1B04032937).

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Correspondence to Michael Th. Rassias.

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Park, C., Rassias, M.T. Additive functional equations and partial multipliers in \(C^*\)-algebras. RACSAM 113, 2261–2275 (2019). https://doi.org/10.1007/s13398-018-0612-y

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Keywords

  • Partial multiplier
  • \(C^*\)-algebra
  • Hyers–Ulam stability
  • Additive functional equation
  • \(C^*\)-ternary algebra
  • Lie \(C^*\)-algebra
  • \(JC^*\)-algebra

Mathematics Subject Classification

  • 46L05
  • 43A22
  • 39B52
  • 39B62