Inequalities for partial determinants of accretive block matrices

Let A = [ A i , j ] i , j = 1 m ∈ M m ( M n ) be an accretive block matrix. We write det 1 and det 2 for the first and second partial determinants, respectively. In this paper, we show that ∥ det 1 ( Re A ) ∥ ≤ ∥ ( tr ( | A | ) m ) m I n ∥ and ∥ det 2 ( Re A ) ∥ ≤ ∥ ( tr ( | A | ) n ) n I m ∥ hold for any unitarily invariant norm ∥ ⋅ ∥ . The two inequalities generalize some known results related to partial determinants of positive-semidefinite block matrices.