New Jensen’s Type Inequalities for Differentiable Log-Convex Functions of Selfadjoint Operators in Hilbert Spaces
DOI:
https://doi.org/10.5644/SJM.07.1.07Keywords:
Selfadjoint operators, positive operators, Jensen's inequality, convex functions, functions of selfadjoint operatorsAbstract
Some new Jensen's type inequalities for differentiable log-convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided.
2000 Mathematics Subject Classification. 47A63, 47A99
Downloads
References
S. S. Dragomir, Gr¨uss’ type inequalities for functions of selfadjoint operators in Hilbert spaces, Preprint, RGMIA Res. Rep. Coll., 11 (e) (2008), Art. 11. [ONLINE: http://www.staff.vu.edu.au/RGMIA/v11(E).asp].
S. S. Dragomir, Some new Gr¨uss’ type inequalities for functions of selfadjoint operators in Hilbert spaces, Preprint RGMIA Res. Rep. Coll., 11 (e) (2008), Art. 12. [ONLINE: http://www.staff.vu.edu.au/RGMIA/v11(E).asp].
S. S. Dragomir, Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces, Preprint RGMIA Res. Rep. Coll., 11 (e) (2008), Art.15 [ONLINE: http://www.staff.vu.edu.au/RGMIA/v11(E).asp].
S. S. Dragomir, Some Jensen type inequalities for log-convex functions of selfadjoint operators in Hilbert spaces, Preprint RGMIA Res. Rep. Coll., 13(e) (2010), Art. 2. [ONLINE: http://rgmia.org/v13(E).php].
T. Furuta, J. Mi´ci´c Hot, J. Peˇcari´c and Y. Seo, Mond-Peˇcari´c, Method in Operator Inequalities. Inequalities for Bounded Selfadjoint Operators on a Hilbert Space, Element, Zagreb, 2005.
A. Matkovi´c, J. Peˇcari´c and I. Peri´c, A variant of Jensen’s inequality of Mercer’s type for operators with applications, Linear Algebra Appl., 418 (2–3) (2006), 551–564.
C. A. McCarthy, cp, Israel J. Math., 5 (1967), 249-271.
J. Mi´ci´c, Y.Seo, S.-E. Takahasi and M. Tominaga, Inequalities of Furuta and MondPeˇcari´c, Math. Ineq. Appl., 2 (1999), 83–111.
D. S. Mitrinovi´c, J. Peˇcari´c and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.
B. Mond and J. Peˇcari´c, Convex inequalities in Hilbert space, Houston J. Math., 19 (1993), 405–420.
B. Mond and J. Peˇcari´c, On some operator inequalities, Indian J. Math., 35 (1993), 221–232.
B. Mond and J. Peˇcari´c, Classical inequalities for matrix functions, Utilitas Math., 46 (1994), 155–166.
