Shift operators and their classification
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911972256120832 |
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| author | Carvalho, Maria Darji, Udayan B. Varandas, Paulo |
| author_facet | Carvalho, Maria Darji, Udayan B. Varandas, Paulo |
| contents | We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We classify vast families of these shift operators, including the ones generated by orthogonal, diagonalizable, rotation or hyperbolic matrices. and this classification yields verifiable conditions which we use to construct concrete examples of shift operators with a variety of dynamical properties. As a consequence, we show that, for large classes of shift operators, generalized hyperbolicity is equivalent to the shadowing property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20890 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shift operators and their classification Carvalho, Maria Darji, Udayan B. Varandas, Paulo Dynamical Systems Primary 37C50, 47B37, 37B65, Secondary 47B33, 47B01, We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We classify vast families of these shift operators, including the ones generated by orthogonal, diagonalizable, rotation or hyperbolic matrices. and this classification yields verifiable conditions which we use to construct concrete examples of shift operators with a variety of dynamical properties. As a consequence, we show that, for large classes of shift operators, generalized hyperbolicity is equivalent to the shadowing property. |
| title | Shift operators and their classification |
| topic | Dynamical Systems Primary 37C50, 47B37, 37B65, Secondary 47B33, 47B01, |
| url | https://arxiv.org/abs/2407.20890 |