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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2409.01167 |
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| _version_ | 1866910587001241600 |
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| author | Contino, Maximiliano Gallardo-Gutierrez, Eva |
| author_facet | Contino, Maximiliano Gallardo-Gutierrez, Eva |
| contents | We address the existence of non-trivial closed invariant subspaces of operators $T$ on Banach spaces whenever their square $T^2$ have or, more generally, whether there exists a polynomial $p$ with $\mbox{deg}(p)\geq 2$ such that the lattice of invariant subspaces of $p(T)$ is non-trivial. In the Hilbert space setting, the $T^2$-problem was posed by Halmos in the seventies and in 2007, Foias, Jung, Ko and Pearcy conjectured it could be equivalent to the \emph{Invariant Subspace Problem}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on a Halmos problem Contino, Maximiliano Gallardo-Gutierrez, Eva Functional Analysis We address the existence of non-trivial closed invariant subspaces of operators $T$ on Banach spaces whenever their square $T^2$ have or, more generally, whether there exists a polynomial $p$ with $\mbox{deg}(p)\geq 2$ such that the lattice of invariant subspaces of $p(T)$ is non-trivial. In the Hilbert space setting, the $T^2$-problem was posed by Halmos in the seventies and in 2007, Foias, Jung, Ko and Pearcy conjectured it could be equivalent to the \emph{Invariant Subspace Problem}. |
| title | A note on a Halmos problem |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2409.01167 |