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arXiv · 2506.07226

Tightening Bounds on the Numerical Radius for Hilbert Space Operators

Maryam Jalili·Hamid Reza Moradi
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Abstract

Let $S$ be a bounded linear operator on a Hilbert space. We show that if $S$ is accretive (resp. dissipative the sense that $\frac{S-{{S}^{*}}}{2i}$ is positive) in the sense that $\frac{S+{{S}^{*}}}{2}$ is positive, then \[\frac{\sqrt{3}}{3}\left\| S \right\|\le \omega \left( S \right),\] where $\left\| \cdot \right\| $ and $\omega \left( \cdot \right)$ denote the operator norm and the numerical radius, respectively.

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Maryam Jalili, Hamid Reza Moradi. 2025-06-08. Tightening Bounds on the Numerical Radius for Hilbert Space Operators. https://doi.org/10.7153/jmi-2025-19-61

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