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• W2997415086 abstract "Let $A$ be a positive bounded linear operator acting on a complex Hilbert space $big(mathcal{H}, langle cdotmid cdotrangle big)$. Let $omega_A(T)$ and ${|T|}_A$ denote the $A$-numerical radius and the $A$-operator seminorm of an operator $T$ acting on the semi-Hilbertian space $big(mathcal{H}, {langle cdotmid cdotrangle}_Abig)$ respectively, where ${langle xmid yrangle}_A := langle Axmid yrangle$ for all $x, yinmathcal{H}$. In this paper, we show that begin{equation*}label{m1} tfrac{1}{4}|T^{sharp_A} T+TT^{sharp_A}|_Ale omega_A^2left(Tright) le tfrac{1}{2}|T^{sharp_A} T+TT^{sharp_A}|_A. end{equation*} Here $T^{sharp_A}$ is denoted to be a distinguished $A$-adjoint operator of $T$. Moreover, a considerable improvement of the above inequalities is proved. This allows to compute the $mathbb{A}$-numerical radius of the operator matrix $begin{pmatrix} I&T 0&-I end{pmatrix}$ where $mathbb{A}= text{diag}(A,A)$. In addition, several $A$-numerical radius inequalities for semi-Hilbertian space operators are also established." @default.
• W2997415086 created "2020-01-10" @default.
• W2997415086 creator A5036304418 @default.
• W2997415086 date "2020-01-02" @default.
• W2997415086 modified "2023-09-27" @default.
• W2997415086 title "Some numerical radius inequalities for semi-Hilbert space operators" @default.
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• W2997415086 hasPublicationYear "2020" @default.
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