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A Kowalski–Słodkowski theorem for 2-local \(^*\)-homomorphisms on von Neumann algebras

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Abstract

It is established that every (not necessarily linear) 2-local \(^*\)-homomorphism from a von Neumann algebra into a C\(^*\)-algebra is linear and a \(^*\)-homomorphism. In the setting of (not necessarily linear) 2-local \(^*\)-homomorphism from a compact C\(^*\)-algebra we prove that the same conclusion remains valid. We also prove that every 2-local Jordan \(^*\)-homomorphism from a JBW\(^*\)-algebra into a JB\(^*\)-algebra is linear and a Jordan \(^*\)-homomorphism.

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Acknowledgments

We thank the anonymous referees for their valuable suggestions.

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Authors and Affiliations

  1. Departamento de Matematicas, Facultad de Ciencias Sociales y de la Educacion, Universidad de Cadiz, 11405, Jerez de la Frontera, Spain

    Maria Burgos

  2. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Francisco J. Fernández-Polo, Jorge J. Garcés & Antonio M. Peralta

  3. Department of Mathematics, College of Science, King Saud University, P.O.Box 2455-5, Riyadh, 11451, Kingdom of Saudi Arabia

    Antonio M. Peralta

Authors
  1. Maria Burgos
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  2. Francisco J. Fernández-Polo
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  3. Jorge J. Garcés
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  4. Antonio M. Peralta
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Corresponding author

Correspondence to Antonio M. Peralta.

Additional information

Authors partially supported by the Spanish Ministry of Science and Innovation, D.G.I. project no. MTM2011-23843, and Junta de Andalucía Grant FQM375. The fourth author extends his appreciation to the Deanship of Scientific Research at King Saud University (Saudi Arabia) for funding the work through research group no. RG-1435-020.

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Burgos, M., Fernández-Polo, F.J., Garcés, J.J. et al. A Kowalski–Słodkowski theorem for 2-local \(^*\)-homomorphisms on von Neumann algebras. RACSAM 109, 551–568 (2015). https://doi.org/10.1007/s13398-014-0200-8

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  • DOI: https://doi.org/10.1007/s13398-014-0200-8

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