Department of Mathematics, School of Mathematics and Computer Science, Damghan University, Damghan, Iran
10.22091/maa.2026.17465.1067
Abstract
To address the limitations of classical subadditive bounds, we establish refined angle-dependent estimates for the numerical radius of Hamiltonian block operator matrices on Hilbert spaces. Using the rotational Cartesian identity, we derive a general angle-dependent bound and its simplified phase-coupled form, which explicitly captures the interaction between the Hermitian off-diagonal blocks. We further develop mean--difference formulations and, in the positive semidefinite case, obtain a closed-form refinement. The Hamiltonian--skew-Hamiltonian decomposition is then used to extend the resulting estimates to arbitrary bounded block operators. Finally, we identify commuting settings in which the phase-coupled bounds are exact and illustrate the effectiveness of the proposed estimates through numerical examples.
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