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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 4

Weighted $\delta$-numerical radius and weighted $\delta$-Crawford number functions

Zameddin İsmailov(KARADENIZ TECHNICAL UNIVERSITY)0000-0001-5193-5349
Elif Otkun Çevik(AVRASYA ÜNİVERSİTESİ)0000-0001-8506-1889
Pages
—
Publication Date
2025-12-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results obtained not only extend certain known results in the literature but also provide a variety of useful techniques that may contribute to further developments in this field.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we investigate several important algebraic and smoothness properties of the weighted $\delta$-numerical radius and the weighted $\delta$-Crawford number functions.
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Key Findings & Data:We also derive estimates of the upper and lower bounds of these weighted functions.
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Conclusion & Impact:The results obtained not only extend certain known results in the literature but also provide a variety of useful techniques that may contribute to further developments in this field.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:weighted $\delta$-numerical radius · weighted $\delta$-Crawford number · sectorial operator

Abstract

In this study, we investigate several important algebraic and smoothness properties of the weighted $\delta$-numerical radius and the weighted $\delta$-Crawford number functions. We also derive estimates of the upper and lower bounds of these weighted functions. Particular attention is paid to the sectorial case of the operators under consideration. The results obtained not only extend certain known results in the literature but also provide a variety of useful techniques that may contribute to further developments in this field.

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Cite This Article

İsmailov, Z., Çevik, E. O. (2025). Weighted $\delta$-numerical radius and weighted $\delta$-Crawford number functions. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 4. https://doi.org/10.15672/hujms.1753320

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References (28)

  1. A. Abu-Omar, F. Kittaneh, A generalization of the numerical radius, Linear Algebra Appl. 569, 323-334, 2019.
  2. N. Altwaijry, K. Feki and N. Minculete, Further inequalities for the weighted numerical radius of operators, Math. 10 (19), Article ID 3576, 2022.
  3. A. Ammar, A. Frakis and F. Kittaneh, Weighted numerical radius inequalities for operators and $2\times 2$ operator matrices, Kyungpook Math. J. 65, 63-75, 2025.
  4. W. Bani-Domi, F. Kittaneh, Norm and numerical radius inequalities for Hilbert space operators, Linear Multilinear Algebra 69 (5), 934-945, 2021.
  5. Y. Bedrani, F. Kittaneh and M. Sababheh, Numerical radii of accretive matrices, Linear Multilinear Algebra 69 (5), 957-970, 2020.
  6. Y.M. Berezansky, Z.G. Sheftel and G.F. Us, Functional Analysis, V.I. Birkhäuser Basel, Berlin, 1966.
  7. P. Bhunia, S.S. Dragomir, M.S. Moslehian and K. Paul, Lectures on numerical radius inequalities, Infosys Science Foundation Series, New York: Springer, 2022.
  8. X. Chi, P. Li, The weighted numerical radius in Hilbert $C^{\ast}$-modules, Filomat 38 (2), 437-448, 2024.
  9. C. Conde, M. Sababheh and H.R. Moradi Some weighted numerical inequalities, arXiv:2204.07620, 2022.
  10. N.P. Dekker, Joint Numerical Range and Joint Spectrum of Hilbert Space Operators, Thesis, University of Amsterdam; 1969.
  11. S.S. Dragomir, Inequalities for the numerical radius of linear operators in Hilbert spaces, Springer, Cham, 2013.
  12. F. Gao, X. Liu, Inequalities for the weighted A-numerical radius of semi-Hilbertian space operators, Oper. Matrices 17 (2), 343-354, 2023.
  13. K.E. Gustafson and D.K.M. Rao, Numerical range: The field of values of linear operators and matrices, Springer-Verlag, New York, 1997.
  14. P.R. Halmos, A Hilbert space problem book, New York: Springer-Verlag, 1982.
  15. Z.I. Ismailov and P. Ipek Al, Generalizations of numerical radius, Crawfor number and numerical index functions in the weighted case, Filomat 39 (11), 3817-3832, 2025.
  16. L. Khadkhuu, D. Tsedenbayar, Spectral properties of $ReV$ and $ImV$, Mong. Math. J. 19, 73-78, 2015.
  17. L. Khadkhuu, D. Tsedenbayar, On the numerical range and numerical radius of the Volterra operator, Izv. Irkutsk. Gos. Univ. Ser. Mat. 24, 102-108, 2018.
  18. F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math. 168 (1), 73-80, 2005.
  19. F. Kittaneh, M.S. Moslehian and T. Yamazaki, Cartesian decomposition and numerical radius inequalities, Linear Algebra Appl. 471, 117-1125, 2023.
  20. F. Kittaneh and H.R. Moradi, Cauchy-Schwarz type inequalities and applications to numerical radius inequalities, Math. Inequal. Appl. 23 (3), 46-53, 2015.
  21. R.K. Nayak, Weighted numerical radius inequalities for operator and operator matrices, Acta Sci. Math.(Szeged) 90 (1-2), 193-206, 2024.
  22. M. Sababheh, C. Conde and H.R. Moradi, A convex-block approach to numerical radius inequalities, Funct. Anal. Appl. 57 (1), 26-30, 2023.
  23. S.A. Sammour, F. Kittaneh and M. Sababheh, A geometric approach to numerical radius inequalities, Linear Algebra Appl. 652, 1-17, 2022.
  24. A. Sheikhhosseini, M. Khosravi and M. Sababheh, The weighted numerical radius, Ann. Funct. Anal. 13 (1), 15 pp., 2022.
  25. J.G. Stampfli, The norm of a derivation, Pacific J. Math. 33, 737-747, 1970.
  26. P.Y. Wu and H. Gau, Numerical ranges of Hilbert space operators, Cambridge University Press, 2021.
  27. A. Zamani, The Weighted Hilbert-Schmidt numerical radius, Linear Algebra Appl. 675, 225-243, 2023.
  28. L. Khadkhuu, D. Tsedenbayar, Spectral properties of $ReV$ and $ImV$, Mong. Math. J. 19, 73-78, 2015.