Upper Bounds for the Numerical Radius of Off-Diagonal 2 × 2 Operator Matrices

Najla Altwaijry () and Silvestru Sever Dragomir
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Najla Altwaijry: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Silvestru Sever Dragomir: Applied Mathematics Research Group, ISILC, Victoria University, P.O. Box 14428, Melbourne, VIC 8001, Australia

Mathematics, 2025, vol. 13, issue 21, 1-18

Abstract: We establish multiple novel upper estimates for the numerical radius associated with off-diagonal operator matrices defined on a complex Hilbert space H . The operators considered have a specific structure, with zero diagonal entries and anti-diagonal entries given by a bounded linear operator C and the adjoint of another, D ★ . The primary contribution is a set of inequalities that connect the square of the numerical radius to expressions involving the norms of these constituent operators. As applications, we specialize our main results to obtain refined inequalities for two significant cases: when D is the adjoint of C , where C and D represent the real and imaginary components of one operator T .

Keywords: numerical radius; off-diagonal operator matrix; bounded linear operators; Hilbert spaces; real and imaginary parts of operators; adjoint operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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