A note on self-commutators of Volterra operator and its square

Authors

  • Lkhamjav Khadkhuu Department of Mathematics, School of Arts and Sciences, National University of Mongolia, Ulaanbaatar, Mongolia
  • Dashdondog Tsedenbayar Department of Mathematics, School of Applied Sciences, Mongolian University of Science and Technology, Ulaanbaatar, Mongolia

DOI:

https://doi.org/10.5564/jasea.v3i1.2455

Keywords:

Volterra operator, operator norm, self-commutator

Abstract

Let V be the classical Volterra operator on L2(0, 1). The quadratic forms and their applications are used in many branches of mathematics. In this area of mathematics have studied many properties for concrete operator such as the numerical range. In recent year, the concept of Volterra operator has attached the serious attention of many researchers. In this paper, we compute the operator norm of self-commutators of V and its square. We also study the length of arc and the area of numerical range of V.

Abstract
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Author Biographies

Lkhamjav Khadkhuu, Department of Mathematics, School of Arts and Sciences, National University of Mongolia, Ulaanbaatar, Mongolia

The Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences,
Ulaanbaatar, Mongolia

Dashdondog Tsedenbayar, Department of Mathematics, School of Applied Sciences, Mongolian University of Science and Technology, Ulaanbaatar, Mongolia

The Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar, Mongolia

References

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P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton, 1982. https://doi.org/10.1007/978-1-4684-9330-6

D. Kershaw, Operator norms of powers of the Volterra operator, Journal of Integral Equations and Applications 11 (1999), pp. 351–362. https://doi.org/10.1216/jiea/1181074282

L. Khadkhuu and D. Tsedenbayar, On the numerical range and numerical radius of the Volterra operator, The Bulletin of Irkutsk State University, Series Mathematics, vol. 24 (2018), pp.102-108. https://doi.org/10.26516/1997-7670.2018.24.102

L. Khadkhuu and D. Tsedenbayar, A note about Volterra operator, Mathematica Slovaca, 68 (2018), pp. 1-4, https://doi.org/10.1515/ms-2017-0173

L. Khadkhuu and D. Tsedenbayar, On the numerical range and operator norm of V 2, Operatrors and Matrices, vol. 14 (2020), pp. 251-259, https://doi.org/10.7153/oam-2020-14-18

Yu. Lyubich and D. Tsedenbayar, The norms and singular numbers of polynomials of the classical Volterra operator, Studia Mathematica, vol. 199 (2010), pp. 171-184, https://doi.org/10.4064/sm199-2-3

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Published

2022-12-31

How to Cite

[1]
L. Khadkhuu and D. Tsedenbayar, “A note on self-commutators of Volterra operator and its square”, J. appl. sci. eng., A, vol. 3, no. 1, pp. 11–16, Dec. 2022.

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