Generalized reverse Cauchy inequality and applications to operator means
Generalized reverse Cauchy inequality and applications to operator means
Let σ be an operator mean in the sense of Kubo-Ando and let ∇ α be a weighted arithmetric mean.If Tr(Aσ B) Tr(A∇ α B -max{α,1 -α}|A -B|) holds for all positive semidefinite matrices A,B , then there exists β ∈ [0,1] such that σ = ∇ β .