Fischer type determinantal inequalities for accretive-dissipative matrices

Let A={bmatrix} A_{11} &A_{12} A_{21} & A_{22} {bmatrix} be an $n\times n$ accretive-dissipative matrix, $k$ and l be the orders of $A_{11}$ and $A_{22}$, respectively, and let $m=\min \{k,l\}$. Then $$\mathrm{\mid }\det A\mathrm{\mid }\le a\mathrm{\mid }\det A_{11}\mathrm{\mid }\cdot \mathrm{\mid }\det A_{22}\mathrm{\mid },$$ where $a={{array}{l l} 2^{3m/2}, & $\text{if}$ m\le n/3; 2^{n/2}, & $\text{if}$ n/3<m\le n/2. {array}.$ This improves a result of Ikramov.