Some Convergence Theorems for Operator Sequences

11 Apr 2019  ·  Mustafayev Heybetkulu ·

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. read more

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