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arXiv · 2602.04134

Refined upper bounds for the numerical radius via weighted operator means

Shankhadeep Mondal·Ram Narayan Mohapatra·Kasun Tharuka Dewage
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Abstract

We establish a parameterized family of upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space, based on weighted expressions involving the modulus of an operator and its adjoint. The proposed estimates encompass a known numerical-radius inequality as a particular symmetric case, while optimization over the weight parameter provides additional flexibility and can lead to sharper bounds. Under suitable structural assumptions on the associated auxiliary operators, we further derive corresponding spectral-radius estimates. The weighted approach is also extended to $2\times2$ off-diagonal operator matrices. Finally, we examine sharpness and equality cases and provide explicit finite-dimensional examples illustrating the obtained estimates.

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Shankhadeep Mondal, Ram Narayan Mohapatra, Kasun Tharuka Dewage. 2026-02-04. Refined upper bounds for the numerical radius via weighted operator means. https://arxiv.org/abs/2602.04134

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