A counterexample shows a tetrablock contraction admits a tetrablock-isometric lift while violating a prior necessary condition, so the rational dilation question for tetrablock contractions remains unresolved.
Curto, Applications of several complex variables to multiparamet er spectral theory , Surveys of some recent results in operator theory, Vol
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Rational dilation of tetrablock contractions revisited
A counterexample shows a tetrablock contraction admits a tetrablock-isometric lift while violating a prior necessary condition, so the rational dilation question for tetrablock contractions remains unresolved.