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

  • Choonkil Park
  • Michael Th. Rassias
Original Paper
  • 7 Downloads

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).

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 

Notes

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).

Compliance with ethical standards

Competing interests

The authors declare that they have no competing interests.

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Copyright information

© The Royal Academy of Sciences, Madrid 2018

Authors and Affiliations

  1. 1.Research Institute for Natural SciencesHanyang UniversitySeoulRepublic of Korea
  2. 2.Institute of MathematicsUniversity of ZurichZurichSwitzerland
  3. 3.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  4. 4.Institute for Advanced Study, Program in Interdisciplinary StudiesPrincetonUSA

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