A note on self-commutators of Volterra operator and its square
DOI:
https://doi.org/10.5564/jasea.v3i1.2455Keywords:
Volterra operator, operator norm, self-commutatorAbstract
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.
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References
E. B. Davies, Linear Operators and Their Spectra, Cambridge Studies in Advanced Mathematics, Cambridge University Press, (106), 2007.
K. E. Gustafson and D. K. M. Rao, Numerical Range, Springer-Verlag, New York, Inc., 1997. https://doi.org/10.1007/978-1-4613-8498-4
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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