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

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

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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Authors and Affiliations

  1. Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Republic of Korea

    Choonkil Park

  2. Institute of Mathematics, University of Zurich, 8057, Zurich, Switzerland

    Michael Th. Rassias

  3. Moscow Institute of Physics and Technology, Institutskiy per, d. 9, Dolgoprudny, Russia, 141700

    Michael Th. Rassias

  4. Institute for Advanced Study, Program in Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ, 08540, USA

    Michael Th. Rassias

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  1. Choonkil Park
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  2. Michael Th. Rassias
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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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  • DOI: https://doi.org/10.1007/s13398-018-0612-y

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