Some matrix power and Karcher means inequalities involving positive linear maps

Hajmohamadi, Monire; Lashkaripour, Rahmatollah; Bakherad, Mojtaba

doi:10.2298/fil1807625h

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2021

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“…For more improvements and refinements on the above inequalities see [7,14,15] and references therein. Let σ be an operator mean with the representing function f .…”

Section: Introductionmentioning

confidence: 99%

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New generalized inequalities using arbitrary operator means and their duals

Nasiri

Bakherad

2021

AUCMCS

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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 constant. We also generalize the above inequality for two arbitrary means $\sigma_{1},\sigma_{2}$ which lie between $\sigma$ and $\sigma^{\perp}$.

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“…For more improvements and refinements on the above inequalities see [7,14,15] and references therein. Let σ be an operator mean with the representing function f .…”

Section: Introductionmentioning

confidence: 99%

“…with h = M m is the Kantorovich constant. The authors in [5] generalized inequality (7) for the higher powers as follows:…”

Section: Introductionmentioning

confidence: 99%