Some Numerical Radius Inequalities Using Maximization

Abstract

A key norm that sheds light on how operators behave on complex matrix spaces is the numerical radius. In this article, the main findings include extensions of Kittaneh’s inequalities, which establish a connection between the operator norm and the numerical radius. Also, we extended existing findings by applying operator generalizations of the Cauchy-Schwarz inequality to further investigate inequalities involving powers of matrices and their mixed forms. Further, we give constraints for the unitarily invariant norms of the Hadamard product of matrices, concentrating on those whose numerical radius is
limited to unity. The findings of this paper advance the general understanding and provide fresh viewpoints and instruments for examining operator behaviour and contribute to the broader understanding of matrix norms and their interrelationships.