Unitarily equivalent bilateral weighted shifts with operator weights
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916338454233088 |
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| author | Buchała, Michał |
| author_facet | Buchała, Michał |
| contents | We study unitarily equivalent bilateral weighted shifts with operator weights. We establish a general characterization of unitary equivalence of such shifts under the assumption that the weights are quasi-invertible. We prove that under certain assumptions unitary equivalence of bilateral weighted shifts with operator weights defined on $ \mathbb{C}^{2} $ can always be given by a unitary operator with at most two non-zero diagonals. We provide examples of unitarily equivalent shifts with weights defined on $ \mathbb{C}^{k} $ such that every unitary operator, which intertwines them has at least $ k $ non-zero diagonals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08770 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitarily equivalent bilateral weighted shifts with operator weights Buchała, Michał Functional Analysis 47B37, 47B02 We study unitarily equivalent bilateral weighted shifts with operator weights. We establish a general characterization of unitary equivalence of such shifts under the assumption that the weights are quasi-invertible. We prove that under certain assumptions unitary equivalence of bilateral weighted shifts with operator weights defined on $ \mathbb{C}^{2} $ can always be given by a unitary operator with at most two non-zero diagonals. We provide examples of unitarily equivalent shifts with weights defined on $ \mathbb{C}^{k} $ such that every unitary operator, which intertwines them has at least $ k $ non-zero diagonals. |
| title | Unitarily equivalent bilateral weighted shifts with operator weights |
| topic | Functional Analysis 47B37, 47B02 |
| url | https://arxiv.org/abs/2402.08770 |