[Sharpening a result by E.B. Davies and B. Simon]
E.B. Davies and B. Simon have shown (among other things) the following result: if T is an matrix such that its spectrum is included in the open unit disc and if , where E stands for endowed with a certain norm , then where stands for the resolvent of T at point λ. Here, we improve this inequality showing that under the same hypotheses (on the matrix T), , for all such that .
E.B. Davies et B. Simon ont montré (entre autres résultats) la chose suivante : soit T, une matrice telle que son spectre soit inclus dans le disque et soit (E étant muni d'une certaine norme ). Alors où désigne la résolvante de T prise au point λ. Nous améliorons ici cette dernière inégalité à travers le résultat suivant : sous les mêmes conditions (portant sur la matrice T), pour tout tel que , on a .
Accepted:
Published online:
Rachid Zarouf 1
@article{CRMATH_2009__347_15-16_939_0, author = {Rachid Zarouf}, title = {Une am\'elioration d'un r\'esultat de {E.B.} {Davies} et {B.} {Simon}}, journal = {Comptes Rendus. Math\'ematique}, pages = {939--942}, publisher = {Elsevier}, volume = {347}, number = {15-16}, year = {2009}, doi = {10.1016/j.crma.2009.04.012}, language = {fr}, }
Rachid Zarouf. Une amélioration d'un résultat de E.B. Davies et B. Simon. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 939-942. doi : 10.1016/j.crma.2009.04.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.012/
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