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Matrix semigroups whose ring commutators have real spectra are realizable

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Abstract

We study matrix semigroups in which ring commutators have real spectra. We prove that irreducible semigroups with this property are simultaneously similar to semigroups of real-entried matrices. We also obtain a structure theorem for compact groups satisfying the property under investigation.

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Acknowledgments

M. Mastnak, H. Radjavi: Supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada, Discovery Grants 371994-2014 and 8809-2002-RGPIN.

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Correspondence to Mitja Mastnak.

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Communicated by Jan Okninski.

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Mastnak, M., Radjavi, H. Matrix semigroups whose ring commutators have real spectra are realizable. Semigroup Forum 95, 51–65 (2017). https://doi.org/10.1007/s00233-016-9797-6

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  • DOI: https://doi.org/10.1007/s00233-016-9797-6

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