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<p>This paper aims to establish new upper and lower bounds for the Euclidean operator radius of a pair of bounded linear operators on a complex Hilbert space and derive novel upper bounds for the numerical radius, by utilizing the notion of angle between two vectors. Among other numerical radius bounds, it is shown that <Equation ID="Equ27"> <EquationSource Format="TEX">\(\begin{aligned} w_{}(T)\le &amp; \sqrt{ \frac{1+\tau }{4}\Vert TT^*+T^*T\Vert } \quad \text { for some }\tau \in [1/2,1], \end{aligned}\)</EquationSource> </Equation>where <i>w</i>(<i>T</i>) and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Vert T\Vert \)</EquationSource> </InlineEquation> denote the numerical radius and the operator norm of a bounded linear operator <i>T</i>,&#xa0; respectively.</p>

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Euclidean operator radius and numerical radius bounds via the notion of angle between two vectors

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Pintu Bhunia,
  • Suvendu Jana,
  • Fuad Kittaneh

摘要

This paper aims to establish new upper and lower bounds for the Euclidean operator radius of a pair of bounded linear operators on a complex Hilbert space and derive novel upper bounds for the numerical radius, by utilizing the notion of angle between two vectors. Among other numerical radius bounds, it is shown that \(\begin{aligned} w_{}(T)\le & \sqrt{ \frac{1+\tau }{4}\Vert TT^*+T^*T\Vert } \quad \text { for some }\tau \in [1/2,1], \end{aligned}\) where w(T) and \(\Vert T\Vert \) denote the numerical radius and the operator norm of a bounded linear operator T,  respectively.