Inequalities for the Davis-Wielandt Radius of Operators in Hilbert C∗-Modules Space

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DOI: https://doi.org/10.28924/2291-8639-22-2024-196
Published: Oct 31, 2024
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Mohammed Hassaouy, Nordine Bounader, Inequalities for the Davis-Wielandt Radius of Operators in Hilbert C∗-Modules Space, Int. J. Anal. Appl., 22 (2024), 196.

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Mohammed Hassaouy, Nordine Bounader

Abstract

The content of this paper presents a fresh method of studying the Davis–Wielandt radius of bounded operators on Hilbert C∗-modules. Using this method, we arrive at new results that improve upper and lower bounds for the Davis-Wielandt radius and generalize known theorems for bounded operators on Hilbert spaces to bounded adjointable operators on Hilbert C∗-module spaces.

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References

  1. S.S. Dragomir, Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces, Springer, Cham, 2013. https://doi.org/10.1007/978-3-319-01448-7.
  2. K.E. Gustafson, D.K.M. Rao, Numerical Range: The Field of Values of Linear Operators and Matrices, Springer, New York, 1997. https://doi.org/10.1007/978-1-4613-8498-4.
  3. R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991. https://doi.org/10.1017/CBO9780511840371.
  4. S.S. Dragomir, A Survey of Some Recent Inequalities for the Norm and Numerical Radius of Operators in Hilbert Spaces, Banach J. Math. Anal. 1 (2007), 154–175. https://doi.org/10.15352/bjma/1240336213.
  5. F. Kittaneh, M.S. Moslehian, 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.
  6. T. Yamazaki, On Upper and Lower Bounds of the Numerical Radius and an Equality Condition, Stud. Math. 178 (2007), 83–89. https://doi.org/10.4064/sm178-1-5.
  7. P. Bhunia, S. Bag, K. Paul, Numerical Radius Inequalities and Its Applications in Estimation of Zeros of Polynomials, Linear Algebra Appl. 573 (2019), 166–177. https://doi.org/10.1016/j.laa.2019.03.017.
  8. A. Zamani, Some Lower Bounds for the Numerical Radius of Hilbert Space Operators, Adv. Oper. Theory, 2 (2017), 98–107. https://doi.org/10.22034/aot.1612-1076.
  9. C.K. Li, Y.T. Poon, N.S. Sze, Davis-Wielandt Shells of Operators, Oper. Matrices (2008), 341–355. https://doi.org/10.7153/oam-02-20.
  10. P. Bhunia, A. Bhanja, S. Bag, K. Paul, Bounds for the Davis-Wielandt Radius of Bounded Linear Operators, Ann. Funct. Anal. 12 (2020), 18. https://doi.org/10.1007/s43034-020-00102-9.
  11. K. Feki, S.A.O. Ahmed Mahmoud, Davis-Wielandt Shells of Semi-Hilbertian Space Operators and Its Applications, Banach J. Math. Anal. 14 (2020), 1281–1304. https://doi.org/10.1007/s43037-020-00063-0.
  12. A. Zamani, K. Shebrawi, Some Upper Bounds for the Davis-Wielandt Radius of Hilbert Space Operators, Mediterr. J. Math. 17 (2019), 25. https://doi.org/10.1007/s00009-019-1458-z.
  13. M.W. Alomari, On the Davis-Wielandt Radius Inequalities of Hilbert Space Operators, Linear Multilinear Algebra 71 (2022), 1804–1828. https://doi.org/10.1080/03081087.2022.2081308.
  14. I. Kaplansky, Modules Over Operator Algebras, Amer. J. Math. 75 (1953), 839–858. https://doi.org/10.2307/2372552.
  15. M.A. Rieffel, Induced Representations of C ∗ -Algebras, Adv. Math. 13 (1974), 176–257. https://doi.org/10.1016/0001-8708(74)90068-1.
  16. W.L. Paschke, Inner Product Modules Over B ∗ -Algebras, Trans. Amer. Math. Soc. 182 (1973), 443–468. https://doi.org/10.1090/s0002-9947-1973-0355613-0.
  17. E.C. Lance, Hilbert C ∗ -Modules: A Toolkit for Operator Algebraists, Cambridge University Press, 1995. https://doi.org/10.1017/CBO9780511526206.
  18. N.E. Wegge-Olsen, K-Theory and C ∗ -Algebras: A Friendly Approach, Oxford University Press, 1993.
  19. G.J. Murphy, C ∗ -Algebras and Operator Theory, Academic Press, Boston, 1990.
  20. S.F. Moghaddam, A.K. Mirmostafaee, Numerical Radius Inequalities for Hilbert C ∗ -Modules, Math. Bohem. 147 (2022), 547–566. http://dml.cz/dmlcz/151098.
  21. M.H.M. Rashid, Some inequalities for the Euclidean operator radius of two operators in Hilbert C ∗ -Modules space, arXiv:2307.01695 [math.FA] (2023). http://arxiv.org/abs/2307.01695.
  22. G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities, Cambridge University Press, Cambridge, 1988.
  23. F. Kittaneh, Notes on Some Inequalities for Hilbert Space Operators, Publ. Res. Inst. Math. Sci. 24 (1988), 276–293. https://doi.org/10.2977/prims/1195175202.
  24. S. Abramovich, G. Jameson, G. Sinnamon, Refining Jensen’s Inequality, Bull. Math. Soc. Sci. Math. Rouman. 47 (2004), 3–14. https://www.jstor.org/stable/43678937.