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On some inequalities related to linear and bounded operators
Corresponding Author(s) : MIRUNA -DANIELA ROȘU
Student Thinkers and Advanced Research,
Vol. 3 No. 1 (2024): Proceedings of the 7th International Conference XGEN
Abstract
The starting point of this paper is the central results of the article by Al-Dolat and Jaradat, “A refinement of the Cauchy-Schwarz inequality accompanied by new numerical radius upper bounds”. The purpose of this paper was to generalize the results obtained by them and to obtain an improvement of those inequalities. This aspect is concretely presented based on an example. An improvement of the inequality of means was used in the proofs, which led to some better results for inequalities on certain powers of numerical radius of some operators.
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- D. K. M. Rao, K. E. Gustafson, Numerical Range, New York: Editura Springer, 1997.
- McCarthy, „Cp,” Israel J. Math., pp. 249-271, 1967.
- S. S. Dragomir, „Power inequalities for the numerical radius of a product of two operators in Hilbert space,” Sarajevo J. Math, vol. vol. 5, pp. 269-278, 2009.
- I. Jaradat, M. Al-Dolat, „A refinement of the Cauchy-Schwarz inequality accompanied by new numerical radius upper bounds,” Filomat, Vol. %1 din %2vol. 37, nr. 3, pp. 971-977, 2023.
- F. Kittaneh, „A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix,” Studia Math, vol. vol. 158, pp. 11-17, 2003.
- V. I. Istrățescu, Introducere în teoria operatorilor liniari, București: Editura Academiei Republicii Socialiste România, 1975.
- P. Y. W. H.-L. G, Kuo-Zhong Wang, „Crawford number of powers of a matrix,” Linear Algebra and its Applications, 2010.
References
D. K. M. Rao, K. E. Gustafson, Numerical Range, New York: Editura Springer, 1997.
McCarthy, „Cp,” Israel J. Math., pp. 249-271, 1967.
S. S. Dragomir, „Power inequalities for the numerical radius of a product of two operators in Hilbert space,” Sarajevo J. Math, vol. vol. 5, pp. 269-278, 2009.
I. Jaradat, M. Al-Dolat, „A refinement of the Cauchy-Schwarz inequality accompanied by new numerical radius upper bounds,” Filomat, Vol. %1 din %2vol. 37, nr. 3, pp. 971-977, 2023.
F. Kittaneh, „A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix,” Studia Math, vol. vol. 158, pp. 11-17, 2003.
V. I. Istrățescu, Introducere în teoria operatorilor liniari, București: Editura Academiei Republicii Socialiste România, 1975.
P. Y. W. H.-L. G, Kuo-Zhong Wang, „Crawford number of powers of a matrix,” Linear Algebra and its Applications, 2010.