By developing Buzano type inequalities in semi-Hilbertian spaces, we obtain several <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$A_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-numerical radius inequalities for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$2\times 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>×</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> block matrices, where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$A_{0}\mathbf {=}\left( \begin{array}{cc} A & 0 \\ 0 & A\\ \end{array} \right) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>A</mi> <mn>0</mn> </msub> <mo>=</mo> <mfenced close=")" open="("> <mrow> <mtable> <mtr> <mtd> <mi>A</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow /> <mn>0</mn> </mrow> </mtd> <mtd> <mi>A</mi> </mtd> </mtr> </mtable> </mrow> </mfenced> </mrow> </math></EquationSource> </InlineEquation> is a <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> diagonal block matrix, whose each diagonal entry is a positive bounded linear operator A on a complex Hilbert space. These inequalities improve and generalize some previously related inequalities. We also deduce several improved A-numerical radius inequalities for semi-Hilbertian space operators.

Buzano type inequalities in semi-Hilbertian spaces with applications

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发表日期：

2026年1月6日

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Messaoud Guesba,
Pintu Bhunia

摘要

By developing Buzano type inequalities in semi-Hilbertian spaces, we obtain several $A_{0}$ $A_{0}$ -numerical radius inequalities for $2\times 2$ $2 \times 2$ block matrices, where $A_{0}\mathbf {=}\left( \begin{array}{cc} A & 0 \\ 0 & A\\ \end{array} \right) $ $A_{0} = (\begin{matrix} A & 0 \\ 0 & A \end{matrix})$ is a $2\times 2$ $2 \times 2$ diagonal block matrix, whose each diagonal entry is a positive bounded linear operator A on a complex Hilbert space. These inequalities improve and generalize some previously related inequalities. We also deduce several improved A-numerical radius inequalities for semi-Hilbertian space operators.