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<p>In this manuscript, we establish a series of novel inequalities involving the <i>A</i>-joint numerical radii and <i>A</i>-joint operator norms of <i>d</i>-tuple operators. These inequalities serve to establish both lower and upper bounds for the <i>A</i>-joint numerical radii of <i>d</i>-tuple operators, encompassing their sum and product. Additionally, we delve into the exploration of <i>A</i>-joint numerical radius inequalities applicable to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\times n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>×</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation> operator matrices, where the matrix entries consist of <i>d</i>-tuple operators. From these inequalities, we derive pertinent Euclidean operator radius inequalities. Furthermore, our investigation extends to the derivation of <i>A</i>-joint operator norm inequalities specific to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n\times n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>×</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation> operator matrices. This comprehensive analysis contributes valuable insights into the interplay between <i>A</i>-joint numerical radius and <i>A</i>-joint operator norm, shedding light on the intricate relationships within the realm of <i>d</i>-tuple operators and their matrix representations.</p>

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Joint A-Numerical Radii of 0perators in Semi-Hilbertian Spaces

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Fuad Kittaneh,
  • M. H. M Rashid,
  • Satyajit Sahoo

摘要

In this manuscript, we establish a series of novel inequalities involving the A-joint numerical radii and A-joint operator norms of d-tuple operators. These inequalities serve to establish both lower and upper bounds for the A-joint numerical radii of d-tuple operators, encompassing their sum and product. Additionally, we delve into the exploration of A-joint numerical radius inequalities applicable to \(n\times n\) n × n operator matrices, where the matrix entries consist of d-tuple operators. From these inequalities, we derive pertinent Euclidean operator radius inequalities. Furthermore, our investigation extends to the derivation of A-joint operator norm inequalities specific to \(n\times n\) n × n operator matrices. This comprehensive analysis contributes valuable insights into the interplay between A-joint numerical radius and A-joint operator norm, shedding light on the intricate relationships within the realm of d-tuple operators and their matrix representations.