论文标题
Katznelson-Tzafriri定理周围的一些发展
Some developments around the Katznelson-Tzafriri theorem
论文作者
论文摘要
本文是Katznelson和Tzafriri在1986年证明的一篇关于发展的调查文章，表明$ \ lim_ {n \ to \ infty} \ | t^n（i-t）\ | = 0 $如果$ t $是Banach空间上的电力运算符，$σ（t）\ cap \ t \ subseteq \ {1 \} $。随后证明了原始定理的许多变化和后果，我们提供了操作者理论的这一分支。
This paper is a survey article on developments arising from a theorem proved by Katznelson and Tzafriri in 1986 showing that $\lim_{n\to\infty} \|T^n(I-T)\| =0$ if $T$ is a power-bounded operator on a Banach space and $σ(T) \cap \T \subseteq \{1\}$. Many variations and consequences of the original theorem have been proved subsequently, and we provide an account of this branch of operator theory.
