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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
@article{KJM_2018_42_4_a8,
     author = {Akram Babri Bajmaeh and Mohsen Erfanian Omidvar},
     title = {Some {Inequalities} for the {Numerical} {Radius} and {Rhombic} {Numerical} {Radius}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {569 },
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a8/}
}
TY  - JOUR
AU  - Akram Babri Bajmaeh
AU  - Mohsen Erfanian Omidvar
TI  - Some Inequalities for the Numerical Radius and Rhombic Numerical Radius
JO  - Kragujevac Journal of Mathematics
PY  - 2018
SP  - 569 
VL  - 42
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a8/
LA  - en
ID  - KJM_2018_42_4_a8
ER  - 
%0 Journal Article
%A Akram Babri Bajmaeh
%A Mohsen Erfanian Omidvar
%T Some Inequalities for the Numerical Radius and Rhombic Numerical Radius
%J Kragujevac Journal of Mathematics
%D 2018
%P 569 
%V 42
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a8/
%G en
%F KJM_2018_42_4_a8
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/