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<p>Several numerical radius inequalities in the framework of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_434_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebras are proved in this paper. These results, which are based on an extension of the Buzano inequality for elements in a pre-Hilbert <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_434_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-module, generalize earlier numerical radius inequalities. An expression for the <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_434_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebra-valued norm based on the numerical radius is also given.</p>

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New estimates for numerical radius in \(C^*\)-algebras

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • Ali Zamani

摘要

Several numerical radius inequalities in the framework of \(C^*\) C ∗ -algebras are proved in this paper. These results, which are based on an extension of the Buzano inequality for elements in a pre-Hilbert \(C^*\) C ∗ -module, generalize earlier numerical radius inequalities. An expression for the \(C^*\) C ∗ -algebra-valued norm based on the numerical radius is also given.