numerical radius inequalities for products of hilbert space operators

We introduce some numerical radius inequalities for products of two hilbert space operators. among other inequalities, it is shown that if s, t ∈ b(h) and st = t s∗ , then ω(st) ≤ ω(s)ω(t) + 1 2 ds sup θ∈r deiθt +e−iθt ∗ , where ds = inf λ∈c ∥s − λi∥. also, we show that if s, t ∈ b(h) and s be self-adjointable, then ω(st) ≤(2∥s) − min λ∈σ(s) |λ| (ω(t)