Operator Norm-Numerical Radius Gaps for Analytic Function of Hilbert Space Operators

Yıl 2024, Cilt: 12 Sayı: 1, 80 - 85, 30.04.2024

Pembe Ipek Al , Rukiye Öztürk Mert , Zameddin İsmailov

Öz

In this study, some estimates are obtained by means of the number of differences between the operator norm of the analytic functions of the linear bounded Hilbert space operator and the numerical radius, and the difference numbers of the powers of the corresponding Hilbert space operators. Firstly, these evaluations are made for the polynomial functions of the linear bounded Hilbert space operator. Later, this topic is generalized for the analytical functions of the linear bounded Hilbert space operator. In the end, two general results are proved.

Anahtar Kelimeler

Analytic functions of operator, Numerical radius, Operator norm

Kaynakça

• [1] T. M. W. Alomari, S. Sahoo and M. Bakherad, Further numerical radius inequalities, J. Math. Inequal., 16, 1 (2022), 307-326.
• [2] W. Bani-Domi and F. Kittaneh, Refined and generalized numerical radius inequalities for 22 operator matrices, Linear Algebra Appl., 624 (2021), 364-386.
• [3] Y. M. Berezansky, Z. G. Sheftel and G. H. Us, Functional Analysis, Birkhauser, 1th printing, Berlin, 1996.
• [4] P. Bhunia and K. Paul, New upper bounds for the numerical radius of Hilbert space operators, Bull. Sci. Math., 167 (2021), 1-11.
• [5] P. Bhunia, K. Paul and R. K. Nayak, Sharp inequalities for the numerical radius of Hilbert space operators and operator matrices, Math. Inequal. Appl., 24 (2021), 167-183.
• [6] M. Demuth, Mathematical aspect of physics with non-selfadjoint operators, List of open problem, American Institute of Mathematics Workshop Germany, (8-12 June 2015).
• [7] S. S. Dragomir, Inequalities for the Numerical Radius of Linear Operators in Hilbert Space, Springer, 1th printing, Chem, 2013.
• [8] K. E. Gustafson and D. K. M. Rao, Numerical Range: The Field Of Values Of Linear Operators And Matrices, Springer, 1th printing, New York, 1997.
• [9] P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, 1th printing, New York, 1967.
• [10] F. Kittaneh, A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix, Studia Math., 158 (2003), 11-17.
• [11] F. Kittaneh,Numerical radius inequalities for Hilbert space operators, Studia Math., 168 (2005), 73-80.
• [12] M. H. M Rashid and N. H. Altaweel, Some generalized numerical radius inequalities for Hilbert space operators, J. Math. Inequal., 16, 2 (2022), 541-560.
• [13] T. Yamazaki, On upper and lower bounds of the numerical radius and equality condition, Studia Math., 178 (2007), 83-89.