Geodesic
Squaring a reverse AM-GM inequality
Minghua Lin1
1 Department of Applied Mathematics University of Waterloo Waterloo, ON, N2L 3G1, Canada
Studia Mathematica, Tome 215 (2013) no. 2, pp. 187-194

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $A , B$ be positive operators on a Hilbert space with $0 m \le A, B \le M$. Then for every unital positive linear map $\varPhi $, $$ \varPhi ^2((A+B)/2)\le K^2(h)\varPhi ^{2}(A\mathbin {\sharp } B), $$ and $$ \varPhi ^2((A+B)/2)\le K^2(h)(\varPhi (A)\mathbin {\sharp } \varPhi (B))^{2}, $$ where $A\mathbin {\sharp } B$ is the geometric mean and $K(h)={(h+1)^2/(4h)}$ with $h=M/m$.
DOI : 10.4064/sm215-2-6
Keywords: positive operators hilbert space every unital positive linear map varphi varphi varphi mathbin sharp varphi varphi mathbin sharp varphi where mathbin sharp geometric mean

Minghua Lin 1

1 Department of Applied Mathematics University of Waterloo Waterloo, ON, N2L 3G1, Canada 
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Minghua Lin. Squaring a reverse AM-GM inequality. Studia Mathematica, Tome 215 (2013) no. 2, pp. 187-194. doi: 10.4064/sm215-2-6

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