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EnglishIn this paper we direct attention at bounded families of complex n×n-matrices. In order to study their asymptotic behaviour, we recall from [Linear Algebra Appl. 322 (2001) 162] the concept of limit spectrum-maximizing product and show that nondefective families always admit such limit products. Then we consider defective families. In [loc. cite] we proved that, for finite families of 2×2-matrices, defectivity is equivalent to the existence of defective such limit products. This result led us to conjecture the validity of this property also for higher dimensions n 3. Here, instead, by making use of the results obtained by Bousch and Mairesse [J. Am. Math. Soc. 15 (2002) 77] that disproved the well-known Finiteness Conjecture, we find some counterexamples to our conjecture in [loc. cite] for all n 3.
| Titolo: | On the limit products of a family of matrices |
| Autori: | |
| Data di pubblicazione: | 2003 |
| Rivista: | |
| Abstract: | In this paper we direct attention at bounded families of complex n×n-matrices. In order to study their asymptotic behaviour, we recall from [Linear Algebra Appl. 322 (2001) 162] the concept of limit spectrum-maximizing product and show that nondefective families always admit such limit products. Then we consider defective families. In [loc. cite] we proved that, for finite families of 2×2-matrices, defectivity is equivalent to the existence of defective such limit products. This result led us to conjecture the validity of this property also for higher dimensions n 3. Here, instead, by making use of the results obtained by Bousch and Mairesse [J. Am. Math. Soc. 15 (2002) 77] that disproved the well-known Finiteness Conjecture, we find some counterexamples to our conjecture in [loc. cite] for all n 3. |
| Handle: | http://hdl.handle.net/11697/14333 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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