A family of $2 \times 2$ tetrablock contractions with non-commuting fundamental operators
math.FA2026-05v1license
Abstract
In this note, we provide a family of 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.
Cite
@article{arxiv.2605.29835,
title = {A family of $2 \times 2$ tetrablock contractions with non-commuting fundamental operators},
author = {Mainak Bhowmik},
journal= {arXiv preprint arXiv:2605.29835},
year = {2026}
}