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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.23099 |
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| _version_ | 1866910898996641792 |
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| author | Cabezas, Eric Saavedra, Manuel |
| author_facet | Cabezas, Eric Saavedra, Manuel |
| contents | We introduce the super-shadowing property in linear dynamics, where pseudotrajectories are approximated by sequences of the form $(λ_nT^nx)$, with $(λ_n)_n$ being complex scalars. For compact operators on Banach spaces, we characterize the operators that possess the positive super-shadowing property and the positive limit super-shadowing property. Additionally, we demonstrate that no surjective isometric operator on a separable Banach space $X$ with $\text{dim}(X)>1$ can exhibit the positive super-shadowing property. Finally, we provide some results on upper frequently supercyclic and reiteratively supercyclic operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Super-Shadowing and Supercyclicity Cabezas, Eric Saavedra, Manuel Functional Analysis Dynamical Systems We introduce the super-shadowing property in linear dynamics, where pseudotrajectories are approximated by sequences of the form $(λ_nT^nx)$, with $(λ_n)_n$ being complex scalars. For compact operators on Banach spaces, we characterize the operators that possess the positive super-shadowing property and the positive limit super-shadowing property. Additionally, we demonstrate that no surjective isometric operator on a separable Banach space $X$ with $\text{dim}(X)>1$ can exhibit the positive super-shadowing property. Finally, we provide some results on upper frequently supercyclic and reiteratively supercyclic operators. |
| title | Super-Shadowing and Supercyclicity |
| topic | Functional Analysis Dynamical Systems |
| url | https://arxiv.org/abs/2503.23099 |