New results are presented for the \((2,2)\) selfadjoint block operator \(K= \left(\begin{smallmatrix} A&B\\ B^*&C \end{smallmatrix}\right)\) on \(H_1\oplus H_2\), where \(A: H_1\to H_1\), \(B: H_2\to H_1\), \(C: H_2\to H_2\), \(A\), \(C\) selfadjoint, \(A\), \(B\) bounded. It is assumed that \(C\) has a spectral gap \(\Delta\). It is known that if the Riccati equation \[ XA- CX+ XBX= B^*\tag{i} \] has a bounded solution \(X\), then the graph \(G(X)\) of \(X\) reduces the operator \(K\) [cf. S. Albeverio, K. A. Makarov and A. K. Motovilov, Can. J. Math. 55, No. 3, 449–503 (2003; Zbl 1074.47007)]. The authors prove that if the spectrum of \(K_{G(X)}\) lies in \(\Delta\), then \[ \| X\|\leq \| B\|/\text{dist}(\sigma(K_{G(X)}),\sigma(C))\tag{ii} \] and \[ \|\tan\theta\|\leq \| B\|/\text{dist}(\sigma(K_{G(X)}),\sigma(C)),\tag{iii} \] where \(\theta\) is the operator angle between \(H_1\) and \(G(X)\). Stronger results hold when \(\Delta\) is finite, \(\sigma(A)\subseteq\Delta\), and \(\| B\|\) is small. For example, if \[ \| B\|^2<|\Delta|\text{dist}(\sigma(A), \sigma(C)), \] then (i) has a unique solution \(X\) such that the spectrum of \(K_{G(K)}\) is a proper closed subset of \(\Delta\) and (ii), (iii) hold.