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Squaring a reverse AM-GM inequality

Minghua Lin — 2013

Studia Mathematica

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.

A treatment of a determinant inequality of Fiedler and Markham

Minghua Lin — 2016

Czechoslovak Mathematical Journal

Fiedler and Markham (1994) proved det H ^ k k det H , where H = ( H i j ) i , j = 1 n is a positive semidefinite matrix partitioned into n × n blocks with each block k × k and H ^ = ( tr H i j ) i , j = 1 n . We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove det ( I n + H ^ ) det ( I n k + k H ) 1 / k .

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