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Keywords:
bounded linear operator; numerical radius; operator norm; inequality
bounded linear operator; numerical radius; operator norm; inequality
Summary:
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 $0\le t\le 1$.
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