A note on a gap result for norms of semigroups of matrices
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- 作者：Yung-Yih Lur
- 关键词：Semigroups of matrices ; Generalized spectral radius ; Joint spectral radius
- 刊名：Linear Algebra and its Applications
- 出版年：2006
- 出版时间：1 December 2006
- 年：2006
- 卷：419
- 期：2-3
- 页码：368-372
- 全文大小：91 K
文摘
Let · be a matrix norm and Σ be a bounded set of n × n complex matrices. For each m = 1, 2, …, let , where Σm = {A1A2Am: Ai Σ}. Bell proved that there is a gap in the possible growth of if Σ consists of finitely many n × n complex matrices. In this note, based on a lemma by Elsner, we give an elementary proof of Bell’s theorem in bounded case.