Generalized Estimation of Numerical Radius for the off-Diagonal 2×2 Operator Matrices and Its Application (Journal of Mathematical Study, 2025)
We give some generalized upper bounds for the numerical radius of off-diagonal 2×2 operator matrices. These inequalities are mainly based on the extensionBuzano inequality and the generalized Young inequality. And our bounds refine andgeneralize the existing related upper bounds. Moreover, the conclusion is applied tothe non-monic operator polynomials and gives a new bound for the eigenvalues ofthese operator polynomials.