On Notions of Expansivity for Operators on Locally Convex Spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911494723076096 |
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| author | Bernardes Jr., Nilson C. Martínez-Giménez, Félix Rodenas, Francisco |
| author_facet | Bernardes Jr., Nilson C. Martínez-Giménez, Félix Rodenas, Francisco |
| contents | We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fréchet sequence spaces. Moreover, we give a partial answer to a problem proposed by Bernardes et al. in J. Funct. Anal. 288 (2025), Paper No. 110696, by obtaining complete characterizations of the uniformly expansive weighted shifts on Köthe sequence spaces. Some general properties of the various concepts of expansivity in linear dynamics and several concrete examples are also presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_12410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Notions of Expansivity for Operators on Locally Convex Spaces Bernardes Jr., Nilson C. Martínez-Giménez, Félix Rodenas, Francisco Functional Analysis Dynamical Systems Primary 37B05. Secondary 46A45, 47B37, 47A16 We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fréchet sequence spaces. Moreover, we give a partial answer to a problem proposed by Bernardes et al. in J. Funct. Anal. 288 (2025), Paper No. 110696, by obtaining complete characterizations of the uniformly expansive weighted shifts on Köthe sequence spaces. Some general properties of the various concepts of expansivity in linear dynamics and several concrete examples are also presented. |
| title | On Notions of Expansivity for Operators on Locally Convex Spaces |
| topic | Functional Analysis Dynamical Systems Primary 37B05. Secondary 46A45, 47B37, 47A16 |
| url | https://arxiv.org/abs/2509.12410 |