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Continued Fraction Representations of the Generalized Operator Entropy Cover

Continued Fraction Representations of the Generalized Operator Entropy

By: Sarra Ahallal,  Ali Kacha and  Said Mennou  
Open Access
|Nov 2023

References

  1. ANDO, T.: Topics on operator inequalities, Ryukyu University. Lecture Note Series, 1978.
  2. AGLER, J.—MCCARTHY, J. E.—YOUNG, N. J.: Operator monotone functions and Löwner functions of several variables, Ann. Math. 176 (2012), 1783–1826.
  3. DINH, T. H.—DUMITRU, R.—FRANCO, J. A.: The matrix power means and interpolations, Adv. Oper. Theory 3 (2018), 647–654.
  4. HIGHAM, N. J.: Functions of Matrices: Theory and Computation.University of Manchister, SIAM, 2008.
  5. ISA, H.—ITO, M.—KAMEI, E.—TOHYAMA, H.—WATANEBE, M.: Relative operator entropy, operator divergence and Shannon inequality, Sci. Math. Japan. 75 (2012), no. 3, 289–298.
  6. JONES, W. B.—THRON, W. J.: Continued Fractions. Analytic Theory and Applications. (With a foreword by Felix E. Browder. With an introduction by Peter Henrici.) Encyclopedia of Mathematics and its Applications Vol. 11, Addison-Wesley Publishing Co., Reading, Mass., 1980.
  7. KACHA, A.—OUNIR, B.—SALHI, S.: Continued fraction expansion of the relative operator entropy and the Tsallis relative entropy, ISOR J. Of Math. Issue 6 (2016), 19–31.
  8. KIM, S.: Operator entropy and fidelity associated with the geometric mean, Linear Algebra Appl. 438 (2013), 2475–2483.
  9. KHOVANSKI, A. N.: The Aplications of Continued Fractions and their Generalisation to Problemes in Approximation Theory. Noordhoff, Groningen, The Netherlands, 1963.
  10. LORENTZEN, L.—WADELAND, H.: Continued Fractions with Applications. Studies in Computational Mathematics Vol 3. North-Holland Publishing Co., Amsterdam, 1992.
  11. MENNOU, S.—CHILLALI, A.—KACHA, A.: Matrix continued fractions expansions of the error function 31. Commun. Math. 1 (2023), 257–271.
  12. MURPHY, G. J.: C∗-Algebras and Operators Theory, Chapter 2, Academic press, INC Harcourt Brace Jovanovich publishers, 1990.
  13. NETTLER, G.: On transcendental numbers whose sum, difference, quotient and product are transcendental numbers, Math. Student 41 (1974), no. 3–4, 339–348.
  14. PETZ, D.: Bregman divergence as relative operator entropy, Acta Math. Hungar. 116 (2007), 127–131.
  15. RAISSOULI, M.—KACHA, A.—SALHI, S: . The continued fractions expansions of real powers of positive definite matrices with applications to matrix means, Arab. J. Sci. Eng. 31 (2006), no.1, 41–56.
  16. SABABHEH, M.: Convexity and matrix means, Linear Algebra Appl. 506 (2016), 588–602.
DOI: https://doi.org/10.2478/tmmp-2023-0024 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 57 - 72
Submitted on: Oct 19, 2022
Published on: Nov 16, 2023
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2023 Sarra Ahallal, Ali Kacha, Said Mennou, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.