Inequalities on the spectral radius, operator norm and numerical radius of the Hadamard weighted geometric mean of positive kernel operators

摘要

Recently, several authors have proved inequalities on the spectral radius rho, operator norm parallel to . parallel to and numerical radius of Hadamard products and ordinary products of nonnegative matrices that define operators on sequence spaces, or of the Hadamard geometric mean and ordinary products of positive kernel operators on Banach function spaces. In the present article we generalize and refine several of these results. In particular, we show that for a Hadamard geometric mean A((1/2)) circle B-(1/2) of positive kernel operators A and B on a Banach function space L, we have