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For initial value problems associated with operator-valued Riccatidifferential equations posed in the space of Hilbert--Schmidt operatorsexistence of solutions is studied. An existence result known for algebraicRiccati equations is generalized and used to obtain the existence of a solutionto the approximation of the problem via a backward Euler scheme. Weak andstrong convergence of the sequence of approximate solutions is establishedpermitting a large class of right-hand sides and initial data.

Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data