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Limitations on the size of semigroups of matrices

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Abstract

If a nonzero linear functional has finite, countable, or bounded range when restricted to an irreducible semigroup \({\mathcal{S}}\) of complex matrices, it is shown that \({\mathcal{S}}\) itself has the same property. Similar results are proven under the hypothesis that a nontrivial ideal of \({\mathcal{S}}\) is finite, countable, or bounded.

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Correspondence to Peter Rosenthal.

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Communicated by Jerome A. Goldstein

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Radjavi, H., Rosenthal, P. Limitations on the size of semigroups of matrices. Semigroup Forum 76, 25–31 (2008). https://doi.org/10.1007/s00233-007-9004-x

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  • DOI: https://doi.org/10.1007/s00233-007-9004-x

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