Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Some remarks on the operator of Foias and Williams

Author(s): Srdjan Petrovic
Journal: Proc. Amer. Math. Soc. 124 (1996), 2807-2811.
MSC (1991): Primary 47A20; Secondary 47B35
MathSciNet review: 1342040
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Abstract | References | Similar articles | Additional information

Abstract: In this paper we study the Foias-Williams operator

$\begin{equation*}T(H_{g})=\begin {pmatrix}S^{*} & H_{g} 0 & S \end {pmatrix} \end{equation*}$

where $g\in L^{\infty }$ , and $H_{g}$ is a Hankel operator with symbol $g$ . We exhibit a relationship between the similarity of $T(H_{g})$ to a contraction and the rate of decay of $\{|g_{n}|\}_{n=0}^{\infty }$ , the absolute values of the Fourier coefficients of the symbol $g$ .

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