Upper bound for spectra of Jensen operator and its application to reverse arithmetic-geometric means. (English) Zbl 1321.47019

Zuo, Hongliang; Fujii, Masatoshi; Fujii, Jun Ichi; Seo, Yuki

Math. Inequal. Appl. 17, No. 2, 641-648 (2014).

M. Krnić et al. [Bull. Malays. Math. Sci. Soc. (2) 35, No. 1, 1–14 (2012; Zbl 1248.47018)] introduced Jensen’s operator and applied it to get some inequalities for means of operators acting on Hilbert spaces. They also established some bounds for the spectrum of Jensen’s operator. In the paper under review, the authors consider Jensen’s operator and establish an optimal upper bound for Jensen’s operator by means of the discrete Jensen’s functional. Based on this, they obtain some reverse weighted arithmetic-geometric operator mean inequalities.

Reviewer: Mohammad Sal Moslehian (Karlstad)

MSC:

47A30	Norms (inequalities, more than one norm, etc.) of linear operators
47A63	Linear operator inequalities

Keywords:

Jensen operator; reverse arithmetic-geometric means; Jensen’s functional