The numerical range of periodic banded Toeplitz operators
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918284391088128 |
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| author | Itzá-Ortiz, Benjamín A. Martínez-Avendaño, Rubén A. Nakazato, Hiroshi |
| author_facet | Itzá-Ortiz, Benjamín A. Martínez-Avendaño, Rubén A. Nakazato, Hiroshi |
| contents | We prove that the closure of the numerical range of a $(n+1)$-periodic and $(2m+1)$-banded Toeplitz operator can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. In contrast to the periodic $3$-banded (or tridiagonal) case, we show an example of a $2$-periodic and $5$-banded Toeplitz operator such that the closure of its numerical range is not equal to the numerical range of a single finite matrix. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_12353 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The numerical range of periodic banded Toeplitz operators Itzá-Ortiz, Benjamín A. Martínez-Avendaño, Rubén A. Nakazato, Hiroshi Functional Analysis 47A12, 15A60 We prove that the closure of the numerical range of a $(n+1)$-periodic and $(2m+1)$-banded Toeplitz operator can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. In contrast to the periodic $3$-banded (or tridiagonal) case, we show an example of a $2$-periodic and $5$-banded Toeplitz operator such that the closure of its numerical range is not equal to the numerical range of a single finite matrix. |
| title | The numerical range of periodic banded Toeplitz operators |
| topic | Functional Analysis 47A12, 15A60 |
| url | https://arxiv.org/abs/2308.12353 |