Let K be a commutative or compact hypergroup. Let \(\mu \) be a bounded complex-valued Borel measure on K, and let \(T_\mu \) be the corresponding convolution operator of \(L^1(K)\). Let S be a bounded linear operator on a Banach space X. We prove that every linear operator \(\Psi : X \rightarrow L^1(K)\) such that \(\Psi S=T_\mu \Psi \) is continuous if and only if the pair \((S,T_\mu )\) has no critical eigenvalues.

中文翻译：

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运算符在超群上与翻译运算符交织的连续性

令K为可交换或紧的超群。令\（\ mu \）为K上的有界复值Borel度量，令\（T_ \ mu \）为\（L ^ 1（K）\）的卷积算子。令S为Banach空间X上的有界线性算子。我们证明每个线性算子\（\ Psi：X \ rightarrow L ^ 1（K）\）使得\（\ Psi S = T_ \ mu \ Psi \）连续且仅当对\（（S， T_ \ mu）\）没有关键特征值。