On the one spectral relation for the analytic function of operator

Volume 15, Issue 4, pp 301--307 https://doi.org/10.22436/jnsa.015.04.05

Publication Date: December 29, 2022 Submission Date: August 10, 2022 Revision Date: September 20, 2022 Accteptance Date: November 12, 2022

Download PDF

Download XML

358 Downloads
910 Views

Authors

Z. I. Ismailov - Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, Trabzon, Turkey. E. O. Cevik - Department of Computer Engineering, Faculty of Engineering and Architecture, Avrasya University, Trabzon, Turkey.

Abstract

In this work, some estimates for the difference number between the operator norm and the spectral radius of analytic functions of linear bounded Hilbert space operators via difference numbers of powers of corresponding Hilbert space operators have been obtained. Firstly, these evaluations for the polynomial functions of the linear bounded Hilbert space operator have been established. Using previous results, this question was later investigated for the exponential, sine, and cosine functions of a given operator. Finally, starting from obtained results, this subject for the analytic functions of the linear bounded Hilbert space operator has been generalized.

Share and Cite

ISRP Style

Z. I. Ismailov, E. O. Cevik, On the one spectral relation for the analytic function of operator, Journal of Nonlinear Sciences and Applications, 15 (2022), no. 4, 301--307

AMA Style

Ismailov Z. I., Cevik E. O., On the one spectral relation for the analytic function of operator. J. Nonlinear Sci. Appl. (2022); 15(4):301--307

Chicago/Turabian Style

Ismailov, Z. I., Cevik, E. O.. "On the one spectral relation for the analytic function of operator." Journal of Nonlinear Sciences and Applications, 15, no. 4 (2022): 301--307

Keywords

Operator norm
spectral radius
analytic functions of operator

MSC

47A10
47A30
47A60
47B02

References

[1] A. Abu-Omar, F. Kittaneh, Estimates for the numerical radius and spectral radius of the Frobenius companion matrix and bounds for the zeros of polynomials, Ann. Funct. Anal., 5 (2014), 56–62

[2] A. Abu-Omar, F. Kittaneh, Notes on some spectral radius and numerical radius inequalities, Studia Math., 227 (2015), 97–109

[3] Y. M. Berezansky, Z. G. Sheftel, G. H. Us, Functional Analysis, Birkh¨auser Verlag, Basel (1966)
- View Article
- Google Scholar

[4] M. Demuth, Mathematical aspect of physics with non-selfadjoint operators: List of open problem, American Institute of Mathematics Workshop, 8 (2015), 12 pages
- View Article
- Google Scholar

[5] A. Dosi, Functional calculus on Noetherian schemes, C. R. Math. Acad. Sci. Paris, 353 (2015), 57–61

[6] A. Dosi, The spectrum of a module along scheme morphism and multi-operator functional calculus, Mosc. Math. J., 21 (2021), 287–323

[7] I. M. Gelfand, Normierte ringe, (German) Rec. Math. [Mat. Sbornik] N. S., 9 (1941), 3–24

[8] F. Kittaneh, Spectral radius inequalities for Hilbert space operators, Proc. Amer. Math. Soc., 134 (2006), 385–390

[9] M. Zima, A theorem on the spectral radius of the sum of two operators and its application, Bull. Austral. Math. Soc., 48 (1993), 427–434

[10] M. Zima, On the local spectral radius in partially ordered Banach spaces, Czechoslovak Math. J., 49 (1999), 835–841

[11] M. Zima, On the local spectral radius of positive operators, Proc. Amer. Math. Soc., 131 (2003), 845–850

[12] M. Zima, Spectral radius inequalities for positive commutators, Czechoslovak Math. J., 64 (2014), 1–10