A family of 2 × 2 tetrablock contractions with non-commuting fundamental operators
Abstract
In this note, we provide a family of 2× 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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