Abstract
In this paper, we give some new lower and upper bounds for relative operator entropy. Making use of them, we present new refinements of some known inequalities involving relative operator entropy.
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Kubo, F., Ando, T.: Means of positive linear operators. Math. Ann. 246, 205–224 (1980)
Zhao, J., Wu, J., Cao, H., Liao, W.: Operator inequalities involving the arithmetic, geometric, Heinz and Heron means. J. Math. Inequal. 8(4), 747–756 (2014)
Clausius, R.: Über die bewegende Kraft der \(\ddot{\rm {W}}\)arme, part I. Part II. Ann. Phys. 79(2), 368–397 (1850)
Nakamura, M., Umegaki, H.: A note on the entropy for operator algebra. Proc. Jpn. Acad. 37, 149–154 (1961)
Umegaki, H.: Conditional expectation in an operator algebra, IV, (entropy and information). Kodai Math. Sem. Rep. 14, 59–85 (1962)
Fujii, J.I., Kamei, E.: Relative operator entropy in noncommutative information theory. Math. Jpn. 34(3), 341–348 (1989)
Furuichi, S.: Inequalities for Tsallis relative entropy and generalized skew information. Linear Multilinear Algebra 59(10), 1143–1158 (2011)
Furuichi, S., Yanagi, K., Kuriyama, K.: Fundamental properties of Tsallis relative entropy. J. Math. Phys. 45(12), 4868–4877 (2004)
Yanagi, K., Kuriyama, K., Furuichi, S.: Generalized Shannon inequalities based on Tsallis relative operator entropy. Linear Algebra Appl. 394(1), 109–118 (2005)
Furuta, T.: Furuta’s inequality and its application to the relative operator entropy. J. Oper. Theory 30(1), 21–30 (1993)
Fujii, J.I., Kamei, E.: Uhlmann’s interpolational method for operator means. Math. Jpn. 34(4), 541–547 (1989)
Zou, L.: Operator inequalities associated with Tsallis relative operator entropy. Math. Inequal. Appl. 18, 401–406 (2015)
Shafiei, M., Ghazanfari, A.G.: Numerous refinements of Pólya and Heinz operator inequalities. Linear Multilinear Algebra 66(4), 852–860 (2018)
Pečarić, J.E., Furuta, T., Mićić Hot, J., Seo, Y.: Mond–Pečarić Method in Operator Inequalities. Inequalities for Bounded Selfadjoint Operators on a Hilbert Space. ELEMENT, Zagreb (2005)
Mićić, J., Pečarić, J., Seo, Y.: Complementary inequalities to inequalities of Jensen and Ando based on the Mond–Pečarić method. Linear Algebra Appl. 318, 87–107 (2000)
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Communicated by Marek Bozejko.
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Soleimani, S., Ghazanfari, A.G. New Refinements of Some Inequalities Involving Relative Operator Entropy. Complex Anal. Oper. Theory 13, 3337–3345 (2019). https://doi.org/10.1007/s11785-019-00938-7
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DOI: https://doi.org/10.1007/s11785-019-00938-7