Geodesic
Jensen's Operator and Applications to Mean Inequalities for Operators in Hilbert Space
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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.
Classification : Primary: 47A63; Secondary: 26D15. 
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     author = {Mario Krnic and Neda Lovricevic and Josip Pecaric},
     title = {Jensen's {Operator} and {Applications} to {Mean} {Inequalities} for {Operators} in {Hilbert} {Space}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_1_a0/}
}
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Mario Krnic; Neda Lovricevic; Josip Pecaric. Jensen's Operator and Applications to Mean Inequalities for Operators in Hilbert Space. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2012_35_1_a0/