Weak Supercyclicity -- An Expository Survey
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912151361290240 |
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| author | Kubrusly, Carlos S. |
| author_facet | Kubrusly, Carlos S. |
| contents | This is an exposition on supercyclicity and weak supercyclicity, especially designed to advance further developments in weakly supercyclicity, which is a recent research field showing significant momentum during the past two decades. For operators on a normed space, the present paper explores the relationship among supercyclicity and three versions of weak supercyclicity, namely, weak l-sequential, weak sequential, and weak supercyclicities, and their connection with strong stability, weak stability, and weak quasistability. A survey of the literature on weak supercyclicity is followed by an analysis of the interplay between supercyclicity and strong stability, as well as between weak supercyclicity and weak stability. A description of the spectrum of weakly l-sequentially supercyclic operators is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02752 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak Supercyclicity -- An Expository Survey Kubrusly, Carlos S. Functional Analysis 47A16, 47A15 This is an exposition on supercyclicity and weak supercyclicity, especially designed to advance further developments in weakly supercyclicity, which is a recent research field showing significant momentum during the past two decades. For operators on a normed space, the present paper explores the relationship among supercyclicity and three versions of weak supercyclicity, namely, weak l-sequential, weak sequential, and weak supercyclicities, and their connection with strong stability, weak stability, and weak quasistability. A survey of the literature on weak supercyclicity is followed by an analysis of the interplay between supercyclicity and strong stability, as well as between weak supercyclicity and weak stability. A description of the spectrum of weakly l-sequentially supercyclic operators is also given. |
| title | Weak Supercyclicity -- An Expository Survey |
| topic | Functional Analysis 47A16, 47A15 |
| url | https://arxiv.org/abs/2405.02752 |