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We present several numerical radius inequalities for Hilbert space operators. More precisely, we prove that if A; B; C; D 2 B.H / and T D A C B D then max.w.A/; w.D// Ä 1 2 .kT k C kT 2 k 1=2 / and max .w.BC // 1=2 ; .w.CB// 1=2 Ä 1 2 .kT k C kT 2 k 1=2 /. We also show that if A 2 B.H / is positive, then w.AX XA/ Ä 1 2 kAk.kXk C kX 2 k 1=2 /: MSC2000: primary 47A62; secondary 46C15, 47A30, 15A24.doi:10.2140/involve.2009.2.471 fatcat:ndndvsryj5cujejwnko3otigk4