Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces

This paper presents new results related to Bombieri’s generalization of Bessel’s inequality in a semi-inner product space induced by positive semidefinite operator A. Specifically, we establish inequalities that generalize the classical Bessel and extend previous this area. Furthermore, our findings have applications study operators on inner spaces, also known as semi-Hilbert contribute deeper understanding their properties applications. Our work has implications for various fields, including functional analysis theory.