Abstract
New numerical radius inequalities for products of two Hilbert space operators are given. Some of our inequalities improve well-known ones. Among other inequalities, it is shown that if A, B is an element of B (94), then w(AB) <= (parallel to A parallel to + D-A)w(B), where D-A = inf(z is an element of C)parallel to A - zI parallel to. Moreover, w(AB) <= parallel to A parallel to w(B) + (1/2)w(AB - BA*). In particular, if AB = BA*, then w(AB) <= parallel to A parallel to w(B).