  For initial value problems associated with operator-valued Riccati
differential equations posed in the space of Hilbert--Schmidt operators
existence of solutions is studied. An existence result known for algebraic
Riccati equations is generalized and used to obtain the existence of a solution
to the approximation of the problem via a backward Euler scheme. Weak and
strong convergence of the sequence of approximate solutions is established
permitting a large class of right-hand sides and initial data.
