Abstract: | In this paper we study the Foias-Williams operator ![\begin{equation*}T(H_{g})=\begin {pmatrix}S^{*} & H_{g} 0 & S \end {pmatrix} \end{equation*}](http://www.ams.org/proc/1996-124-09/S0002-9939-96-03459-4/gif-abstract/img1.gif)
where , and is a Hankel operator with symbol . We exhibit a relationship between the similarity of to a contraction and the rate of decay of , the absolute values of the Fourier coefficients of the symbol . |