Characterization of uniformly asymptotic S-Toeplitz and S-Hankel operators

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.