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arXiv · 2501.06995

Generalized numerical radius inequalities for certain operator matrices

Satyajit Sahoo·Narayan Behera
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Abstract

In this article, a series of new inequalities involving the $q$-numerical radius for $n\times n$ tridiagonal, and anti-tridiagonal operator matrices has been established. These inequalities serve to establish both lower and upper bounds for the $q$-numerical radius of operator matrices. Additionally, we developed $q$-numerical radius inequalities for $n\times n$ circulant, skew circulant, imaginary circulant, imaginary skew circulant operator matrices. Important examples have been used to illustrate the developed inequalities. In this regard, analytical expressions and a numerical algorithm have also been employed to obtain the $q$-numerical radii. We also provide a concluding section, which may lead to several new problems in this area.

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Satyajit Sahoo, Narayan Behera. 2025-01-13. Generalized numerical radius inequalities for certain operator matrices. https://arxiv.org/abs/2501.06995

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