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Concrete Operators

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Mathematical Citation Quotient (MCQ) 2016: 0.38


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On the Commutativity of a Certain Class of Toeplitz Operators

Issam Louhichi
  • Corresponding author
  • King Fahd University of Petroleum & Minerals, Department of Mathematics & Statistics, Dhahran 31261, Saudi Arabia
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/ Fanilo Randriamahaleo
  • Université de Bordeaux, UFR de Mathématiques et Informatique, 351, Cours de la Libération, 33405 Talence, France
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/ Lova Zakariasy
Published Online: 2014-05-01 | DOI: https://doi.org/10.2478/conop-2014-0001

Abstract

One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex place C is to completely describe the commutant of a given Toeplitz operator, that is, the set of all Toeplitz operators that commute with it. Here we shall study the commutants of a certain class of quasihomogeneous Toeplitz operators defined on the harmonic Bergman space.

Keywords : Toeplitz operator; Mellin transform

References

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  • [3] I. Louhichi and N. V. Rao, Roots of Toeplitz operators on the Bergman space. Pacific Journal of Mathematics. Volume 252, Number 1 (2011), 127-144.Web of ScienceGoogle Scholar

  • [4] I. Louhichi and N. V. Rao, Bicommutants of Toeplitz operators, Arch. Matik. Volume 91 (2008), 256-264.Google Scholar

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  • [8] I. Louhichi, Powers and roots of Toeplitz operators, Proc. Amer. Math. Soc. 135, (2007), 1465-1475.Web of ScienceGoogle Scholar

  • [9] I. Louhichi, E. Strouse and L. Zakariasy, Products of Toeplitz operators on the Bergman space, Integral equations Operator Theory 54 (2006), 525-539.Google Scholar

  • [10] I. Louhichi and L. Zakariasy, On Toeplitz operators with quasihomogeneous symbols, Arch. Math. 85 (2005), 248-257.Google Scholar

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  • [12] R. Remmert, Classical Topics in Complex Function Theory, Graduate Texts in Mathematics, Springer, New York, 1998. Google Scholar

About the article

Received: 2014-01-31

Accepted: 2014-04-01

Published Online: 2014-05-01

Published in Print: 2014-01-01


Citation Information: Concrete Operators, ISSN (Online) 2299-3282, DOI: https://doi.org/10.2478/conop-2014-0001.

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© by Issam Louhichi et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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