Inequalities on the spectral radius and the operator norm of hadamard products of positive operators on sequence spaces

Abstract

K. M. R. Audenaert (2010), R. A. Horn and F. Zhang (2010), Z. Huang (2011), A. R. Schep (2011), A. Peperko (2012), and D. Chen and Y. Zhang (2015) have proved inequalities on the spectral radius and the operator norm of Hadamard products and ordinary matrix products of finite and infinite nonnegative matrices that define operators on sequence spaces. In the present article, we extend and refine several of these results, and we also prove some analogues for the numerical radius.