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>2. 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>2.

On the limit products of a family of matrices

ZENNARO, MARINO
2003-01-01

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>2. 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>2.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/1703208
 Avviso

Registrazione in corso di verifica.
La registrazione di questo prodotto non è ancora stata validata in ArTS.

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 11
social impact