Some norm inequalities for accretive Hilbert space operators

New norm inequalities for accretive operators on Hilbert space are given. Among other inequalities, we prove that if \ (A, B B (H) \) and \ (B\) is self-adjoint and also \ (C₌, ₌ (iAB) \) is accretive, then eqnarray* 4 MmM+m AB (AB-BA^*), eqnarray* where \ (M\) and \ (m\) are positive real numbers with \ (M > m\) and \ (C₌, ₌ (A) = (A^* - mI) (MI - A) \). Also, we show that if \ (C₌, ₌ (A) \) is accretive and \ ( (M-m) k A \), then eqnarray* (AB) (2 + k) (A) (B). eqnarray*