Generalized Cauchy–Schwarz Inequalities and A-Numerical Radius Applications

The purpose of this research paper is to introduce new Cauchy–Schwarz inequalities that are valid in semi-Hilbert spaces, which generalizations Hilbert spaces. We demonstrate how these can be employed derive novel A-numerical radius inequalities, where A denotes a positive semidefinite operator complex space. Some our expand upon the existing literature on numerical with space operators, important tools functional analysis. use techniques from theory prove results and highlight some applications findings.