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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some remarks on the operator
of Foias and Williams


Author: 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: 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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Additional Information

Srdjan Petrovic
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: petrovic@iu-math.math.indiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03459-4
PII: S 0002-9939(96)03459-4
Keywords: Polynomially bounded operators, similarity to contractions
Received by editor(s): March 21, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society