Volume 35 • Number 1 • 2012   • Jensen's Operator and Applications to Mean Inequalities for Operators in Hilbert Space Mario Krnic, Neda Lovricevic and Josip Pecaric Abstract. In this paper we consider Jensen's operator, which includes bounded self-adjoint operator on Hilbert space, and investigate its properties. Due to derived properties, we find lower and upper bound for Jensen's operator, which are multiples of non-weighted Jensen's operator. On the other hand, we also establish some bounds for spectra of Jensen's operator by means of discrete Jensen's functional. The obtained results are then applied to operator means. In such a way, we get refinements and conversions of numerous mean inequalities for Hilbert space operators. 2010 Mathematics Subject Classification: Primary: 47A63; Secondary: 26D15. Full text: PDF