Some numerical radius inequality for several semi-Hilbert space operators
Cristian Conde, Kais Feki · Linear and Multilinear Algebra · 2022
The paper deals with the generalized numerical radius of linear operators acting on a complex Hilbert space H, which are bounded with respect to the seminorm induced by a positive operator A on H. Here A is not assumed to be invertible. Mainly, if we denote by ωA(⋅) and ω(⋅) the generalized and the classical numerical radii respectively, we prove that for every A-bounded operator T we have ωA(T)=ω(A1/2T(A1/2)†), where (A1/2)† is the Moore-Penrose inverse of A1/2. In addition, several new inequalities involving ωA(⋅) for single and several operators are established. In particular, by using new techniques, we cover and improve some recent results due to Najafi [Linear Algebra Appl. 2020;588:489–496].