Geodesic
Some Inequalities for the Numerical Radius and Rhombic Numerical Radius
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 569

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In this paper, the definition Rhombic numerical radius is introduced and we present several numerical radius inequalities. Some applications of these inequalities are considered as well. Particular, it is shown that, if $A\in \mathcal B \left( \mathcal{H} \right)$ with the Cartesian decomposition $A=C+iD$ and $r\geq 1$, then \[\begin{aligned} mega^r(A)eq\frac{qrt{2}}{2}{ eftVertvert C+D\rvert^{2 r}+vert C-D\rvert^{2 r}\right\rVert}^{\frac{1}{2}}. \end{aligned}\]
Classification : 47A12 47A30, 47A63
Keywords: Rhombic numerical radius, numerical radius, usual operator norm 
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     author = {Akram Babri Bajmaeh and Mohsen Erfanian Omidvar},
     title = {Some {Inequalities} for the {Numerical} {Radius} and {Rhombic} {Numerical} {Radius}},
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Akram Babri Bajmaeh; Mohsen Erfanian Omidvar. Some Inequalities for the Numerical Radius and Rhombic Numerical Radius. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 569 . http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a8/