Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some upper bounds for the $\mathbb{A}$-numerical radius of $2\times 2$
  block matrices   Let $\mathbb{A}=\left( \begin{array}{cc} A & 0 \\ 0 & A \\ \end{array}
\right)$ be the $2\times2$ diagonal operator matrix determined by a positive
bounded operator $A$. For semi-Hilbertian operators $X$ and $Y$, we first show
that \begin{align*} w^2_{\mathbb{A}}\left(\begin{bmatrix} 0 & X \\ Y & 0
\end{bmatrix}\right) &\leq \frac{1}{4}\max\Big\{{\big\|XX^{\sharp_A} +
Y^{\sharp_A}Y\big\|}_{A}, {\big\|X^{\sharp_A}X + YY^{\sharp_A}\big\|}_{A}\Big\}
+ \frac{1}{2}\max\big\{w_{A}(XY), w_{A}(YX)\big\}, \end{align*} where
$w_{\mathbb{A}}(\cdot)$, ${\|\cdot\|}_{A}$ and $w_{A}(\cdot)$ are the
$\mathbb{A}$-numerical radius, $A$-operator seminorm and $A$-numerical radius,
respectively. We then apply the above inequality to find some upper bounds for
the $\mathbb{A}$-numerical radius of certain $2\times 2$ operator matrices. In
particular, we obtain some refinements of earlier $A$-numerical radius
inequalities for semi-Hilbertian operators. An upper bound for the
$\mathbb{A}$-numerical radius of $2\times 2$ block matrices of semi-Hilbertian
space operators is also given.

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The categories of this paper are: econ
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph