We show that hyperrigidity for a C*-correspondence (A, X) is equivalent to non-degeneracy of the left action of the Katsura ideal \(\mathcal {J}_X\) on X. This extends the work of Kakariadis (Bull Lond Math Soc 45(6):1119–1130, 2013, Theorem 3.3) and Dor-On and Salomon (J Lond Math Soc 98(2):416–438, 2018, Theorem 3.5) who establish this equivalence for discrete graphs as well as the work of Katsoulis and Ramsey (The non-selfadjoint approach to the Hao–Ng isomorphism, arXiv preprint arXiv:1807.11425, 2018, Theorem 3.1), who establish one direction of this equivalence.

我们证明了 C* 对应关系 ( A ,  X ) 的超刚性等效于 Katsura 理想\(\mathcal {J}_X\)在X上的左作用的非简并性。这扩展了 Kakariadis（Bull Lond Math Soc 45(6):1119–1130, 2013, Theorem 3.3）和 Dor-On and Salomon（J Lond Math Soc 98(2):416-438, 2018, Theorem 3.5）的工作他们为离散图建立了这种等价关系，以及 Katsoulis 和 Ramsey 的工作（The non-selfadjoint approach to the Hao-Ng isomorphism，arXiv preprint arXiv:1807.11425, 2018, Theorem 3.1），他们建立了这种等价关系的一个方向。