Une amélioration d'un résultat de E.B. Davies et B. Simon

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• 作者：Rachid Zarouf
• 刊名：Comptes Rendus Mathematique
• 出版年：2009
• 出版时间：August 2009
• 年：2009
• 卷：347
• 期：15-16
• 页码：939-942
• 全文大小：123 K

文摘

E.B. Davies and B. Simon have shown (among other things) the following result: if T is an n×n matrix such that its spectrum σ(T) is included in the open unit disc and if C=sup_k0T^k_E→E, where E stands for endowed with a certain norm ., then R(1,T)_E→EC(3n/dist(1,σ(T)))^3/2 where R(λ,T) 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 λσ(T) such that λ1. To cite this article: R. Zarouf, C. R. Acad. Sci. Paris, Ser. I 347 (2009).