Some numerical radius inequalities for Hilbert space operators

Mohsen Erfanian Omidvar, Mohammad Sal Moslehian, Asdolah Niknam
<span title="2009-10-28">2009</span> <i title="Mathematical Sciences Publishers"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6e2u6r7vnaq5ady7zgkb3kilu" style="color: black;">Involve. A Journal of Mathematics</a> </i> &nbsp;
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.
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