On some inequalities with matrix means

Fu, Xiaohui; Hoa, Dinh Trung

doi:10.1080/03081087.2015.1010472

Cited by 8 publications

(5 citation statements)

References 7 publications

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“…Hoa, Toan and Binh [8] studied some reverse inequalities for arbitrary pair of operator means. Recently, Fu and Hoa [5] extended this result for any power greater than 1, see also [14]. This note intends to extend the operator Pólya-Szegö inequality (1.1) for any arbitrary operator mean.…”

Section: Introductionmentioning

confidence: 82%

An extension of the Pólya--Szegö operator inequality

Hoa

Moslehian

Conde

et al. 2016

Preprint

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Section: Introductionmentioning

confidence: 82%

An extension of the Pólya--Szegö operator inequality

Hoa

Moslehian

Conde

et al. 2016

Preprint

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“…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%

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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“…It should be mentioned that many authors did the similar researches, see (e.g. [6], [8], [9], [11], [14], [17], [18]).…”

Section: Introductionmentioning

confidence: 99%

Some operator inequalities for operator means and positive linear maps

Zhao

2019

Filomat

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In this note, some operator inequalities for operator means and positive linear maps are investigated. The conclusion based on operator means is presented as follows: Let Φ : B(H) → B(K) be a strictly positive unital linear map and h −1 1 I H ≤ A ≤ h 1 I H and h −1 2 I H ≤ B ≤ h 2 I H for positive real numbers h 1 , h 2 ≥ 1. Then for p > 0 and an arbitrary operator mean σ, (Φ(A)σΦ(B)) p ≤ α p Φ p (Aσ * B), where α p = max α 2 (h 1 ,h 2) 4 p , 1 16 α 2p (h 1 , h 2) , α(h 1 , h 2) = (h 1 + h −1 1)σ(h 2 + h −1 2). Likewise, a p-th (p ≥ 2) power of the Diaz-Metcalf type inequality is also established.

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On some inequalities with matrix means

Cited by 8 publications

References 7 publications

An extension of the Pólya--Szegö operator inequality

An extension of the Pólya--Szegö operator inequality

New generalized inequalities using arbitrary operator means and their duals

Some operator inequalities for operator means and positive linear maps

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