Abstract:In this article, we present some operator inequalities via arbitrary operator means and unital positive linear maps. For instance, we show that if $A,B \in {\mathbb B}({\mathscr H}) $ are two positive invertible operators such that $ 0 < m \leq A,B \leq M $ and $\sigma$ is an arbitrary operator mean, then \begin{align*} \Phi^{p}(A\sigma B) \leq K^{p}(h) \Phi^{p}(B\sigma^{\perp} A), \end{align*} where $\sigma^{\perp}$ is dual $\sigma$, $p\geq0$ and $K(h)=\frac{(M+m)^{2}}{4 Mm}$ is the classical Kantorovich c… Show more
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