On the Riccati equations

In this article we give, in terms of so-called Berezin symbols, some necessary conditions for the solvability of the Riccati equation XAX+XB-CX-D=0XAX+XB-CX-D=0 on the set T{\cal T} of all Toeplitz operators on the Hardy space H²(\Bbb D)H^2({\Bbb D}) .