Some developments around the Katznelson-Tzafriri theorem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929490874073088 |
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| author | Batty, Charles Seifert, David |
| author_facet | Batty, Charles Seifert, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_13411 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Some developments around the Katznelson-Tzafriri theorem Batty, Charles Seifert, David Functional Analysis 47A05 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. |
| title | Some developments around the Katznelson-Tzafriri theorem |
| topic | Functional Analysis 47A05 |
| url | https://arxiv.org/abs/2204.13411 |