Novel inequalities refine numerical radius bounds in Hilbert space operators, suggesting improvements in operator analysis.
This paper introduces novel inequalities for the ‐numerical radius of operators. Among our main findings, we prove that for , where denotes the generalized Aluthge transform of . These inequalities refine and extend several existing bounds in the literature. Furthermore, we investigate the ‐numerical radius of several significant classes of operator matrices.
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Gao et al. (2026) studied this question.
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