Abstract
We improve the operator Kantorovich inequality as follows: Let A be a positive operator on a Hilbert space with 0<m≤A≤M. Then for every unital positive linear map Φ, Φ(A−1)2≤((M+m)24Mm)2Φ(A)−2. As a consequence, Φ(A−1)Φ(A)+Φ(A)Φ(A−1)≤(M+m)22Mm.
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