Geodesic
Inequalities involving norm and numeri\nobreak cal radius of Hilbert space operators
Commentationes Mathematicae Universitatis Carolinae, Tome 65 (2024) no. 1, pp. 45-52
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This paper presents several numerical radii and norm inequalities for Hilbert space operators. These inequalities improve some earlier related inequalities. For an operator $A$, we prove that \begin{align*} \omega^{2}(A)\le \Big\| \frac{A^{*}A+AA^{*}}{2} -\frac{1}{2R}\big(( 1-t){{A}^{*}}A+tA{{A}^{*}} -((1-t)(A^{*}A)^{1/2}+( AA^{*})^{1/2} )^{2} \big) \Big\| \end{align*} where $R=\max\{t,1-t\}$ and $0\le t\le 1$.
This paper presents several numerical radii and norm inequalities for Hilbert space operators. These inequalities improve some earlier related inequalities. For an operator $A$, we prove that \begin{align*} \omega^{2}(A)\le \Big\| \frac{A^{*}A+AA^{*}}{2} -\frac{1}{2R}\big(( 1-t){{A}^{*}}A+tA{{A}^{*}} -((1-t)(A^{*}A)^{1/2}+( AA^{*})^{1/2} )^{2} \big) \Big\| \end{align*} where $R=\max\{t,1-t\}$ and $0\le t\le 1$.
DOI : 10.14712/1213-7243.2025.006
Classification : 47A12, 47A30, 47A63
Keywords: bounded linear operator; numerical radius; operator norm; inequality 
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Goudarzi, Nasrollah; Heydarbeygi, Zahra. Inequalities involving norm and numeri\nobreak cal radius of Hilbert space operators. Commentationes Mathematicae Universitatis Carolinae, Tome 65 (2024) no. 1, pp. 45-52. doi: 10.14712/1213-7243.2025.006

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