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arXiv · 1212.5690

On an operator Kantorovich inequality for positive linear maps

Minghua Lin
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Abstract

We improve the operator Kantorovich inequality as follows: Let $A$ be a positive operator on a Hilbert space with $0<m\le A \le M$. Then for every unital positive linear map $Φ$, \[Φ(A^{-1})^2\le (\frac{(M+m)^2}{4Mm})^2Φ(A)^{-2}.\] As a consequence, \[Φ(A^{-1})Φ(A)+Φ(A)Φ(A^{-1}) \le \frac{(M+m)^2}{2Mm}.\]

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Minghua Lin. 2012-12-22. On an operator Kantorovich inequality for positive linear maps. https://arxiv.org/abs/1212.5690

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