In this short paper, we prove that the Bochner integral form of the operator-valued Riccati equation has a unique solution if and only if its mild form has a unique solution. This implies that the mild and Bochner integral forms of this equation are equivalent. The result is obtained through an operator representation argument.

翻译：本文证明了算子值Riccati方程的Bochner积分形式存在唯一解当且仅当其温和形式存在唯一解。这意味着该方程的温和形式与Bochner积分形式等价。该结论通过算子表示论证方法得到。