Well-Posedness of the Bochner Integral Form of Operator-Valued Riccati Equations

Abstract

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.

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