Document Type : Original Article


1 Department of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, Iran

2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tarbiat Modares, Tehran, Iran


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.