호남수학학술지 (Honam Mathematical Journal)

  • 제43권3호
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  • Pages.523-537
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  • 2021
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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BEREZIN NUMBER INEQUALITIES VIA YOUNG INEQUALITY

  • 투고 : 2021.04.12
  • 심사 : 2021.05.25
  • 발행 : 2021.09.25
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초록

In this paper, we obtain some new inequalities for the Berezin number of operators on reproducing kernel Hilbert spaces by using the Hölder-McCarthy operator inequality. Also, we give refine generalized inequalities involving powers of the Berezin number for sums and products of operators on the reproducing kernel Hilbert spaces.

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참고문헌

  1. N. Aronzajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950), 337-404. https://doi.org/10.1090/S0002-9947-1950-0051437-7
  2. M. Bakherad, Some Berezin number inequalities for operator matrices, Czechoslov. Math. J., 68(4) (2018), 997-1009. https://doi.org/10.21136/CMJ.2018.0048-17
  3. M. Bakherad and M.T. Garayev, Berezin number inequalities for operators, Concr. Oper., 6(1) (2019), 33-43. https://doi.org/10.1515/conop-2019-0003
  4. H. Basaran, M. Gurdal and A.N. Guncan, Some operator inequalities associated with Kantorovich and Holder-McCarthy inequalities and their applications, Turkish J. Math., 43(1) (2019), 523-532. https://doi.org/10.3906/mat-1811-10
  5. F.A. Berezin, Covariant and contravariant symbols for operators, Math. USSR-Izvestiya, 6 (1972), 1117-1151. https://doi.org/10.1070/IM1972v006n05ABEH001913
  6. F.A. Berezin, Quantization, Math. USSR-Izvestiya, 8 (1974), 1109-1163. https://doi.org/10.1070/IM1974v008n05ABEH002140
  7. S. S. Dragomir, Vector inequalities for powers of some operators in Hilbert spaces, Filomat, 23(1) (2009), 69-83. https://doi.org/10.2298/FIL0901069D
  8. M. Fujii and R. Nakamoto, Refinements of Holder-McCarthy inequality and Young inequality, Adv. Oper. Theory, 1(2) (2016), 184-188.
  9. M. T. Garayev, Berezin symbols, Holder-McCarthy and Young inequalities and their applications, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 43(2) (2017), 287-295.
  10. M. Garayev, F. Bouzeffour, M. Gurdal and C. M. Yangoz, Refinements of Kantorovich type, Schwarz and Berezin number inequalities, Extracta Math., 35 (2020), 1-20. https://doi.org/10.17398/2605-5686.35.1.1
  11. M. T. Garayev, M. Gurdal and A. Okudan, Hardy-Hilbert's inequality and a power inequality for Berezin numbers for operators, Math. Inequal. Appl., 19 (2016), 883-891.
  12. M. T. Garayev, M. Gurdal and S. Saltan, Hardy type inequaltiy for reproducing kernel Hilbert space operators and related problems, Positivity, 21 (2017), 1615-1623. https://doi.org/10.1007/s11117-017-0489-6
  13. M. T. Garayev, H. Guedri, M. Gurdal and G. M. Alsahli, On some problems for operators on the reproducing kernel Hilbert space, Linear Multilinear Algebra, 69 (11) (2021), 2059-2077. https://doi.org/10.1080/03081087.2019.1659220
  14. M. Garayev, S. Saltan, F. Bouzeffour and B. Aktan, Some inequalities involving Berezin symbols of operator means and related questions, RACSAM Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat., 114(85) (2020), 1-17. https://doi.org/10.1007/s13398-019-00732-2
  15. K. E. Gustafson and D. K. M. Rao, Numerical Range, Springer-Verlag, New York, 1997.
  16. M. Hajmohamadi, R. Lashkaripour and M. Bakherad, Improvements of Berezin number inequalities, Linear Multilinear Algebra, 68(6) (2020), 1218-1229. https://doi.org/10.1080/03081087.2018.1538310
  17. Z. Heydarbeygi and M. Amyari, Some refinements of the numerical radius inequalities via Young inequality, Kragujevac J. Math., 45(2) (2021), 191-202. https://doi.org/10.46793/KgJMat2102.191H
  18. J. A. R. Holbrook, Multiplicative properties of the numerical radius in operator theory, J. Reine Angew. Math., 237 (1969), 166-174.
  19. M. T. Karaev, Berezin symbol and invertibility of operators on the functional Hilbert spaces, J. Funct. Anal., 238 (2006), 181-192. https://doi.org/10.1016/j.jfa.2006.04.030
  20. M. T. Karaev, Reproducing kernels and Berezin symbols techniques in various questions of operator theory, Complex Anal. Oper. Theory, 7 (2013), 983-1018. https://doi.org/10.1007/s11785-012-0232-z
  21. M. Kian, Operator Jensen inequality for superquadratic functions, Linear Algebra Appl., 456 (2014), 82-87. https://doi.org/10.1016/j.laa.2012.12.011
  22. F. Kittaneh, A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix, Studia Math., 158(1) (2003), 11-17. https://doi.org/10.4064/sm158-1-2
  23. F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math., 168(1) (2005), 73-80. https://doi.org/10.4064/sm168-1-5
  24. F. Kittaneh and M. El-Haddad, Numerical radius inequalities for Hilbert space operators II, Studia Math., 182(2) (2007), 133-140. https://doi.org/10.4064/sm182-2-3
  25. F. Kittaneh, M. S. Moslehian and T. Yamazaki, Cartesian decomposition and numerical radius inequalities, Linear Algebra Appl., 471 (2015), 46-53. https://doi.org/10.1016/j.laa.2014.12.016
  26. H. Kober, On the arithmetic and geometric means and on Holder's inequality, Proc. Amer. Math. Soc., 9 (1958), 452-459. https://doi.org/10.1090/S0002-9939-1958-0093564-7
  27. C-S. Lin and Y. J. Cho, On Holder-McCarthy-type inequalities with powers, J. Korean Math. Soc., 39(3) (2002), 351-361. https://doi.org/10.4134/JKMS.2002.39.3.351
  28. S. S. Sahoo, N. Das and D. Mishra, Berezin number and numerical radius inequalities for operators on Hilbert spaces, Advances in Oper. Theory, 5 (2020), 714-727 https://doi.org/10.1007/s43036-019-00035-8
  29. M. Sattari, M. S. Moslehian and T. Yamazaki, Some generalized numerical radius inequalities for Hilbert space operators, Linear Algebra Appl., 470 (2015), 216-227. https://doi.org/10.1016/j.laa.2014.08.003
  30. K. Shebrawi and H. Albadwi, Numerical radius and operator norm inequalities, J. Inequal. Appl., 2009 (2009), Article ID 492154, 11 pages.
  31. R. Tapdigoglu, On the description of invariant subspaces in the space Cn[0, 1], Houston J. Math., 39(1) (2013), 169-176.
  32. R. Tapdigoglu, New Berezin symbol inequalities for operators on the reproducing kernel Hilbert space, Oper. Matrices, (accepted) 2020.
  33. U. Yamanci, and M. Gurdal, On numerical radius and Berezin number inequalities for reproducing kernel Hilbert space, New York J. Math., 23 (2017), 1531-1537.
  34. U. Yamanci, M. Gurdal and M. T. Garayev, Berezin number inequality for convex function in reproducing kernel Hilbert space, Filomat, 31 (2017), 5711-5717. https://doi.org/10.2298/FIL1718711Y
  35. U. Yamanci, R. Tunc and M. Gurdal, Berezin numbers, Gruss type inequalities and their applications, Bull. Malays. Math. Sci. Soc., 43 (2020), 2287-2296. https://doi.org/10.1007/s40840-019-00804-x
  36. A. Zamani, Some lower bounds for the numerical radius of Hilbert space operators, Adv. Oper. Theory, 2(2) (2007), 98-107.