Squaring a reverse AM-GM inequality
Minghua Lin
Studia Mathematica, Tome 215 (2013), p. 187-194 / Harvested from The Polish Digital Mathematics Library
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Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:285724 
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Minghua Lin. Squaring a reverse AM-GM inequality. Studia Mathematica, Tome 215 (2013) pp. 187-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-2-6/