New improvements on numerical radius bounds via the Moore–Penrose inverse

Abstract

Abstract In this paper, we establish several inner product inequalities that characterize the positivity of block operator matrices. By examining specific blocks of positive operator matrices involving the Moore–Penrose inverse, we derive new inner product inequalities that refine recently established bounds. As an application, we further refine certain numerical radius inequalities from the literature. Our findings generalize and extend several well-known results in this field, contributing to ongoing advancements in operator inequalities.