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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.29835 |
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| _version_ | 1866910270116331520 |
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| author | Bhowmik, Mainak |
| author_facet | Bhowmik, Mainak |
| contents | In this note, we provide a family of $2\times 2$ tetrablock contractions that have tetrablock isometric dilation, but the corresponding fundamental operators do not commute. This answers a question raised by Bhattacharyya [Indiana Univ. Math. J. 2014] about the necessity of commuting fundamental operators for a tetrablock contraction to have rational dilation in a negative direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29835 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A family of $2 \times 2$ tetrablock contractions with non-commuting fundamental operators Bhowmik, Mainak Functional Analysis 47A20, 47A13 In this note, we provide a family of $2\times 2$ tetrablock contractions that have tetrablock isometric dilation, but the corresponding fundamental operators do not commute. This answers a question raised by Bhattacharyya [Indiana Univ. Math. J. 2014] about the necessity of commuting fundamental operators for a tetrablock contraction to have rational dilation in a negative direction. |
| title | A family of $2 \times 2$ tetrablock contractions with non-commuting fundamental operators |
| topic | Functional Analysis 47A20, 47A13 |
| url | https://arxiv.org/abs/2605.29835 |