Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and $\left\{ \frac{1}{n}\sum_{i=0}^{n-1}A^{i}TB^{i}% \right\} $. These results are applied to the Toeplitz, composition and model operators. Some related problems are also discussed.

中文翻译：

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算子序列的一些收敛定理

令 $A、$$T$ 和 $B$ 是 Banach 空间上的有界线性算子。本文主要关注寻找序列$\left\{ A^{n}TB^{n}\right\} $ 和$\left\{ \frac{1 的算子范数收敛的一些充要条件}{n}\sum_{i=0}^{n-1}A^{i}TB^{i}% \right\} $. 这些结果应用于 Toeplitz、组合和模型运算符。还讨论了一些相关问题。