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<p>In this paper, we give several upper bounds for the numerical radii of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(2\times 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>×</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> operator matrices. These upper bounds refine and generalize some earlier existing ones. As an application of one of our results, we give new upper bounds for the numerical radii of the sums and the products of two operators.</p>

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Sharp estimates for the numerical radii of \(2\times 2\) operator matrices

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Messaoud Guesba,
  • Fuad Kittaneh

摘要

In this paper, we give several upper bounds for the numerical radii of \(2\times 2\) 2 × 2 operator matrices. These upper bounds refine and generalize some earlier existing ones. As an application of one of our results, we give new upper bounds for the numerical radii of the sums and the products of two operators.