Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-96-03459-4
MathSciNet review: 1342040
Full-text PDF

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 $g$.


References [Enhancements On Off] (What's this?)

  • 1. G. Bennett, Schur multipliers, Duke Math. J. 44 (3) (1977), 603--639. MR 58:12490
  • 2. J. F. Carlson, D. N. Clark, C. Foias, and J. P. Williams, Projective Hilbert ${\mathbb {A}}({\mathbb {D}})$-modules, The New York Journal of Mathematics 1 (1994), 26--38. CMP 94:15
  • 3. C. Foias, and J. P. Williams, On a class of polynomially bounded operators, preprint.
  • 4. P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887--933. MR 42:5066
  • 5. V. Paulsen, Every completely polynomially bounded operator is similar to a contraction, J. Funct. Anal. 55 (1984), 1--17. MR 86c:47021
  • 6. V. Paulsen, C. Pearcy, and S. Petrovi\'{c}, On centered and weakly centered operators, J. Funct. Anal. 128 (1) (1995), 87--101. MR 95k:47026
  • 7. W. Rudin, Some theorems on Fourier coefficients, Proc. Amer. Math. Soc. 10 (1959), 855--859. MR 22:6979
  • 8. H. Shapiro, Extremal Problems for Analytic Functions and Polynomials, Dissertation, MIT, 1952.
  • 9. B. Sz.-Nagy, Completely continuous operators with uniformly bounded iterates, Magyar Tud. Akad. Mat. Kutató Int. Köze 4 (1959), 89--93. MR 21:7436

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A20, 47B35

Retrieve articles in all journals with MSC (1991): 47A20, 47B35


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-96-03459-4
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

American Mathematical Society