  We establish existence and uniqueness for infinite dimensional Riccati
equations taking values in the Banach space L 1 ($\mu$ $\otimes$ $\mu$) for
certain signed matrix measures $\mu$ which are not necessarily finite. Such
equations can be seen as the infinite dimensional analogue of matrix Riccati
equations and they appear in the Linear-Quadratic control theory of stochastic
Volterra equations.
