Opuscula Math. 41, no. 6 (2021), 881-898
https://doi.org/10.7494/OpMath.2021.41.6.881

 
Opuscula Mathematica

μ-Hankel operators on Hilbert spaces

Adolf Mirotin
Ekaterina Kuzmenkova

Abstract. A class of operators is introduced (\(\mu\)-Hankel operators, \(\mu\) is a complex parameter), which generalizes the class of Hankel operators. Criteria for boundedness, compactness, nuclearity, and finite dimensionality are obtained for operators of this class, and for the case \(|\mu| = 1\) their description in the Hardy space is given. Integral representations of \(\mu\)-Hankel operators on the unit disk and on the Semi-Axis are also considered.

Keywords: Hankel operator, \(\mu\)-Hankel operator, Hardy space, integral representation, nuclear operator, integral operator.

Mathematics Subject Classification: 47B25, 47B35.

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  • Adolf Mirotin (corresponding author)
  • ORCID iD https://orcid.org/0000-0001-7340-4522
  • F. Skorina Gomel State University, Department of Mathematics and Programming Technologies, 246019, Sovietskaya, 104, Gomel, Belarus
  • Regional Mathematical Center, Southern Federal University, Rostov-on-Don, 344090 Russia
  • Ekaterina Kuzmenkova
  • F. Skorina Gomel State University, Department of Mathematics and Programming Technologies, 246019, Sovietskaya, 104, Gomel, Belarus
  • Communicated by P.A. Cojuhari.
  • Received: 2021-06-23.
  • Accepted: 2021-08-09.
  • Published online: 2021-11-29.
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Cite this article as:
Adolf Mirotin, Ekaterina Kuzmenkova, μ-Hankel operators on Hilbert spaces, Opuscula Math. 41, no. 6 (2021), 881-898, https://doi.org/10.7494/OpMath.2021.41.6.881

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