Opuscula Math. 38, no. 4 (2018), 573-590
https://doi.org/10.7494/OpMath.2018.38.4.573

 
Opuscula Mathematica

Toeplitz versus Hankel: semibounded operators

Dmitri R. Yafaev

Abstract. Our goal is to compare various results for Toeplitz \(T\) and Hankel \(H\) operators. We consider semibounded operators and find necessary and sufficient conditions for their quadratic forms to be closable. This property allows one to define \(T\) and \(H\) as self-adjoint operators under minimal assumptions on their matrix elements. We also describe domains of the closed Toeplitz and Hankel quadratic forms.

Keywords: semibounded Toeplitz, Hankel and Wiener-Hopf operators, closable and closed quadratic forms.

Mathematics Subject Classification: 47B25, 47B35.

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  • Dmitri R. Yafaev
  • Université de Rennes I, IRMAR, Campus de Beaulieu, 35042 Rennes Cedex, France
  • SPGU, Univ. Nab. 7/9, Saint Petersburg, 199034 Russia
  • Communicated by P.A. Cojuhari.
  • Received: 2017-11-07.
  • Accepted: 2017-12-10.
  • Published online: 2018-04-11.
Opuscula Mathematica - cover

Cite this article as:
Dmitri R. Yafaev, Toeplitz versus Hankel: semibounded operators, Opuscula Math. 38, no. 4 (2018), 573-590, https://doi.org/10.7494/OpMath.2018.38.4.573

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