OICC Press Mathematical Analysis and its Contemporary Applications 5 2 2023 07 01 Characterization of uniformly asymptotic S-Toeplitz and S-Hankel operators 10.30495/maca.2023.1989709.1071 EN Massoud Salehi Sarvestani Department of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, Iran Massoud Amini Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran Journal Article 2023 07 01 In this paper, we show that a shift operator on a separable Hilbert space with infinite multiplicity is strongly approximated by shift operators with finite multiplicities. Moreover, for an arbitrary shift operator S, we introduce the notion of an (asymptotic) S-Hankel operator and study its relation to the class of (asymptotic) S-Toeplitz operators.