New norm and numerical radius bounds for accretive-dissipative operator matrices

Abstract

In operator and matrix theory, obtaining sharper bounds for quantities such as the operator norm and the numerical radius is of central importance. The main goal of this paper is to present new novel bounds that work for the norm and numerical radius of accretive–dissipative operator matrices, with particular emphasis on the interaction between diagonal and off-diagonal blocks. The obtained results are compared with the existing literature, showing that the new bounds provide better estimates than some known results.