Power Bounds for the Numerical Radius of the Off-Diagonal 2 × 2 Operator Matrix

Author:

Altwaijry Najla1ORCID,Dragomir Silvestru Sever2ORCID,Feki Kais3ORCID

Affiliation:

1. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

2. Applied Mathematics Research Group, ISILC, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, Australia

3. Laboratory Physics-Mathematics and Applications (LR/13/ES-22), Faculty of Sciences of Sfax, University of Sfax, Sfax 3018, Tunisia

Abstract

In this paper, we employ a generalization of the Boas–Bellman inequality for inner products, as developed by Mitrinović–Pečarić–Fink, to derive several upper bounds for the 2p-th power with p≥1 of the numerical radius of the off-diagonal operator matrix 0AB*0 for any bounded linear operators A and B on a complex Hilbert space H. While the general matrix is not symmetric, a special case arises when B=A*, where the matrix becomes symmetric. This symmetry plays a crucial role in the derivation of our bounds, illustrating the importance of symmetric structures in operator theory.

Funder

King Saud University, Riyadh, Saudi Arabia

Publisher

MDPI AG

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