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 $$|\det A|\le a|\det A_{11}|\cdot|\det A_{22}|,$$ 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. 
Minghua Lin
math.FA