On the Essential Norm Formulas for Some Operators

摘要

Abstract We prove equivalence of the classical Adamyan-Arov-Krein theorem (Adamyan, Arov and Krein in Mat Sb 86:34–75, 1971) and Mustafayev’s recent result in (Mustafayev in Integr Equ Oper Theory 92:1–21, 2020) about essential norm of Hankel and function of model operators, respectively. We also prove a quantitative version of Bessonov’s compactness theorem for truncated Toeplitz operators.