Energma's research partner announces a second major advancement in operator theory with the publication of a new framework for numerical radius inequalities in complex Hilbert spaces.
Building upon the generalized real and imaginary parts of an operator introduced by Kittaneh and Stojiljković in Journal of Inequalities and Applications, 2026, this study develops a new generalized numerical radius defined through functional parameters. The framework rigorously establishes its properties as a norm on the C*-algebra of bounded linear operators under specified conditions.
The proposed construction unifies and extends a wide range of existing results. By allowing flexibility through functions h and g, the generalized numerical radius reduces to previously known formulations in the literature.
In particular, it encompasses the weighted numerical radius inequalities established by Sheikhhosseini, Khosravi, and Sababheh in Annals of Functional Analysis, 2022, as well as classical numerical radius inequalities developed by Kittaneh in Studia Mathematica, 2005.
Beyond unification, the paper delivers new identities and sharper bounds for the generalized numerical radius. It explores inequalities involving powers of operators and operator matrices, providing refined extensions of earlier results in the field. These contributions strengthen the structural understanding of operator inequalities and expand the analytical tools available for future research.
Through this adaptable and comprehensive framework, we continue to reinforce our position at the forefront of modern mathematical analysis, advancing both theoretical rigor and functional versatility within operator theory.
Talk to one of our solution experts and start the journey.
Book the Call