Generalized reverse Cauchy inequality and applications to operator means

摘要

Let σ be an operator mean in the sense of Kubo-Ando and let . α be a weighted arith- metric mean. If Tr(A σ B) Tr(A . α B . max{ α ,1 . α }|A . B|) holds for all positive semidefi- nite matrices A,B , then there exists β ∈ [0,1] such that σ = . β .