SOME OPERATOR INEQUALITIES IN HILBERT $C^{*}$MODULES VIA THE OPERATOR PERSPECTIVE | ||
| Journal of Algebraic Systems | ||
| دوره 13، شماره 1، تیر 2025، صفحه 89-103 اصل مقاله (152.91 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2023.12626.1677 | ||
| نویسندگان | ||
| Ismail Nikoufar* ؛ Zahra Baghernezhad Shayan | ||
| Department of Mathematics, Payame Noor University, Tehran, Iran. | ||
| چکیده | ||
| Some Hilbert $C^*$-module versions of H$\ddot{o}$lder-McCarthy and H$\ddot{o}$lder type inequalities and their complementary on a Hilbert $C^*$-module are obtained by Seo \cite{seo-2014}. The purpose of this paper is to extend these results for some operator convex (resp. concave) functions on a Hilbert $C^*$-module via the operator perspective approach. By choosing some elementary functions, we reach some new types of inequalities in Hilbert $C^*$-modules. | ||
| کلیدواژهها | ||
| Operator convex function؛ adjointable operators؛ perspective function؛ H$\ddot{o}$lder inequality | ||
| مراجع | ||
|
1. T. Ando and F. Hiai, Ho¨lder type inequalities for matrices, Math. Inequal. Appl., 1 (1998), 1–30.
2. J.-C. Bourin, E.-Y. Lee, M. Fujii and Y. Seo, A matrix reverse Ho¨lder inequality, Linear Algebra Appl., 431 (2009), 2154–2159.
3. M. D. Choi, A schwarz inequality for positive linear maps on C∗-algebras, Illinois J. Math., 18 (1974), 565–574.
4. C. Davis, A Schwarz inequality for convex operator functions, Proc. Amer. Math. Soc., 8 (1957), 42–44.
5. A. Ebadian, I. Nikoufar and M. Eshagi Gordji, Perspectives of matrix convex functions, Proc. Natl. Acad. Sci., 108 (2011), 7313–7314.
6. E. G. Effros, A matrix convexity approach to some celebrated quantum inequalities, Proc. Natl. Acad. Sci. USA., 106 (2009), 1006–1008.
7. J. I. Fujii, M. Fujii, M. S. Moslehian and Y. Seo, Cauchy–Schwarz inequality in semi-inner product C∗-modules via polar decomposition, J. Math. Anal. Appl., 394 (2012), 835–840.
8. J. I. Fujii and E. Kamei, Relative operator entropy in noncommutative information theory, Math. Japonica, 34 (1989), 341–348.
9. T. Furuta, Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators, Linear Algebra Appl., 381 (2004), 219–235.
10. F. Kubo and T. Ando, Means of positive linear operators, Math. Ann., 246 (1980), 205–224.
11. E. C. Lance, Hilbert C∗-Modules, London Math. Soc. Lecture Note Series 210, Cambridge University Press, Cambridge, 1995.
12. J. Mic´ic´, J. Pecˇaric´ and Y. Seo, Complementary inequalities to inequalities of Jensen and Ando based on the Mond–Pecˇaric´ method, Linear Algebra Appl., 318 (2000), 87–107.
13. B. Mond and J. Pecˇaric´, Convex inequalities in Hilbert space, Houston J. Math., 19 (1993), 405–420.
14. I. Nikoufar, A new characterization of the operator perspective, Linear Multilinear Algebra, 70 (2022), 4297–4319.
15. I. Nikoufar, A perspective approach for characterization of Lieb concavity theorem, Demonstr. Math., 49 (2016), 463–469.
16. I. Nikoufar, Improved operator inequalities of some relative operator entropies, Positivity, 24 (2020), 241–251.
17. I. Nikoufar, On operator inequalities of some relative operator entropies, Adv. Math., 259 (2014), 376–383.
18. I. Nikoufar, Operator versions of Shannon type inequality, Math. Ineq. Appl., 19 (2016), 359–367.
19. I. Nikoufar and M. Fazlolahi, Equivalence relations among inequalities for some relative operator entropies, Positivity, 24 (2020), 1503–1518.
20. I. Nikoufar and M. Shamohammadi, The converse of the Loewner–Heinz inequality via perspective, Linear Multilinear Algebra, 66 (2018), 243–249.
23. K. Yanagi, K. Kuriyama and S. Furuichi, Generalized Shannon inequalities based on Tsallis relative operator entropy, Linear Algebra Appl., 394 (2005), 109–118.
24. L. Zou, Operator inequalities associated with Tsallis relative operator entropy, Math. Inequal. Appl., 18 (2015), 401–406
21. W. L. Paschke, Inner product modules over B∗-algebras, Trans. Amer. Math. Soc., 182 (1973), 443–468.
22. Y. Seo, Ho¨lder type inequalities on Hilbert C∗-modules and its reverses, Ann. Funct. Anal., 5 (2014), 1–9 | ||
|
آمار تعداد مشاهده مقاله: 112 تعداد دریافت فایل اصل مقاله: 113 |
||