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arXiv · 2605.29835

A family of $2 \times 2$ tetrablock contractions with non-commuting fundamental operators

Mainak Bhowmik
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Abstract

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.

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BibTeXRIS

Mainak Bhowmik. 2026-05-28. A family of $2 \times 2$ tetrablock contractions with non-commuting fundamental operators. https://doi.org/10.1016/j.laa.2026.05.021

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