Abstract
A semigroup \({\mathfrak{S}}\) of non-negative n × n matrices is indecomposable if for every pair i, j ≤ n there exists \({S\in\mathfrak{S}}\) such that (S) ij ≠ 0. We show that if there is a pair k, l such that \({\{(S)_{kl} : S\in\mathfrak{S}\}}\) is bounded then, after a simultaneous diagonal similarity, all the entries are in [0, 1]. We also provide quantitative versions of this result, as well as extensions to infinite-dimensional cases.
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H. Radjavi, A. Tcaciuc and V. G. Troitsky were supported by NSERC.
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Gessesse, H., Popov, A.I., Radjavi, H. et al. Bounded indecomposable semigroups of non-negative matrices. Positivity 14, 383–394 (2010). https://doi.org/10.1007/s11117-009-0024-5
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DOI: https://doi.org/10.1007/s11117-009-0024-5