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Betterment for estimates of the numerical radii of Hilbert space operators | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 8، دوره 4، شماره 2، 2023، صفحه 161-167 اصل مقاله (336.87 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21907.1122 | ||
| نویسندگان | ||
| Mohammad Davarpanah* 1؛ Hamid Reza Moradi2 | ||
| 1Department of Mathematics, Ferdows Branch, Islamic Azad University, Ferdows, Iran | ||
| 2Department of Mathematics, Payame Noor University (PNU), P.O. Box, 19395-4697, Tehran, Iran | ||
| چکیده | ||
| We give several inequalities involving numerical radii $\omega \left( \cdot \right)$ and the usual operator norm $\|\cdot\|$ of Hilbert space operators. These inequalities lead to a considerable improvement in the well-known inequalities \begin{equation*} \frac{1}{2}\left\| T \right\|\le \omega \left( T \right)\le \left\| T \right\|. \end{equation*} | ||
| کلیدواژهها | ||
| Numerical radius؛ Usual operator norm؛ Inequality؛ Contraction operator | ||
| مراجع | ||
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[1] Invitation to Linear Operators: From Matrices to Bounded Linear Operators on a Hilbert Space, CRC Press, 2001.
[2] P. R. Halmos, A Hilbert space problem book, vol. 17 of Encyclopedia of Mathematics and its Applications, Springer-Verlag, New York-Berlin, second ed., 1982.
[3] F. Kittaneh, A numerical radius inequality and an estimate for the numerical radius of the Frobenius com[1]panion matrix, Studia Math., 158 (2003), pp. 11–17.
[4] , Numerical radius inequalities for Hilbert space operators, Studia Math., 168 (2005), pp. 73–80.
[5] F. Kittaneh and H. R. Moradi, Cauchy-Schwarz type inequalities and applications to numerical radius inequalities, Math. Inequal. Appl., 23 (2020), pp. 1117–1125.
[6] H. R. Moradi, S. Furuichi, Z. Heydarbeygi, and M. Sababheh, Revisiting the Gr¨uss inequality, Oper. Matrices, 15 (2021), pp. 1379–1392.
[7] M. E. Omidvar, H. R. Moradi, and K. Shebrawi, Sharpening some classical numerical radius inequalities, Oper. Matrices, 12 (2018), pp. 407–416.
[8] J. Pecari ˘ c, T. Furuta, J. Mi ´ ci ´ c Hot, and Y. Seo ´ , Mond-Peˇcari´c method in operator inequalities, vol. 1 of Monographs in Inequalities, ELEMENT, Zagreb, 2005. Inequalities for bounded selfadjoint operators on a Hilbert space.
[9] K. E. G. . D. K. M. Rao, Numerical Range: The Field of Values of Linear Operators and Matrices, Univer[1]sitext (UTX), Springer New York, NY, 1997.
[10] S. Sheybani, M. Sababheh, and H. R. Moradi, Weighted Inequalities For The Numerical Radius, Vietnam J. Math., 51 (2023), pp. 363–377. | ||
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