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 is an element of B(H) and B is self-adjoint and also C-m,C-M(iAB) is accretive, then 4 root Mm / M+m & Vert;AB & Vert; <= omega(AB - BA(& lowast;)), where M and m are positive real numbers with M > m and C-m,C-M(A) = (A(& lowast;)- mI)(MI - A). Also, we show that if C-m,C-M(A) is accretive and (M - m) <= k & Vert; A & Vert;, then omega(AB) <= (2 + k)omega(A)omega(B).