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

Abstract

ABSTRACTRecently, several authors have proved inequalities on the spectral radius , operator norm 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 of positive kernel operators A and B on a Banach function space L, we have In the special case we also prove that