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<p>We develop inequalities for the algebraic numerical radius of elements in a unital <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebra <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {A}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">A</mi> </math></EquationSource> </InlineEquation> through the development of inequalities for positive linear functionals. In particular, we deduce several improved lower and upper bounds for the algebraic numerical radius and the equality conditions. In addition, by defining the algebraic Euclidean operator radius of a pair of elements in <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal {A}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">A</mi> </math></EquationSource> </InlineEquation>, we derive several related results.</p>

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Numerical radius and Euclidean operator radius inequalities on \(C^*\)-algebras

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Suvendu Jana,
  • Pintu Bhunia

摘要

We develop inequalities for the algebraic numerical radius of elements in a unital \(C^*\) C ∗ -algebra \(\mathcal {A}\) A through the development of inequalities for positive linear functionals. In particular, we deduce several improved lower and upper bounds for the algebraic numerical radius and the equality conditions. In addition, by defining the algebraic Euclidean operator radius of a pair of elements in \(\mathcal {A}\) A , we derive several related results.