Geodesic
Infinite products and paracontracting matrices
The electronic journal of linear algebra, Tome 2 (1997), pp. 1-8.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In [Linear Algebra Appl., 161:227-263, 1992] the LCP-property of a finite set $\Sigma $of square complex matrices was introduced and studied. A set $\Sigma $is an LCP-set if all left infinite products formed from matrices in $\Sigma $are convergent. It was shown earlier in [Linear Algebra Appl., 130:65-82, 1990] that a set $\Sigma $paracontracting with respect to a fixed norm is an LCP-set. Here a converse statement is proved: If $\Sigma $is an LCP-set with a continuous limit function then there exists a norm such that all matrices in $\Sigma $are paracontracting with respect to this norm. In addition the stronger property of `-paracontractivity is introduced. It is shown that common `-paracontractivity of a set of matrices has a simple characterization. It turns out that in the above mentioned converse statement the norm can be chosen such that all matrices are `-paracontracting. It is shown that for $\Sigma $consisting of two projectors the LCP-property is equivalent to `-paracontractivity, even without requiring continuity.
Classification : 65F10, 47H09, 15A99 
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     title = {Infinite products and paracontracting matrices},
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Beyn, W.-J.; Elsner, L. Infinite products and paracontracting matrices. The electronic journal of linear algebra, Tome 2 (1997), pp. 1-8. http://geodesic.mathdoc.fr/item/ELA_1997__2__a1/