Complementary inequalities to improved AM-GM inequality

Moradi, Hamid Reza; Omidvar, Mohsen Erfanian

doi:10.1007/s10114-017-7118-y

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Cited by 3 publications

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“…The problem of squaring operator inequalities has been studied extensively in the literature. We refer the reader to [4,[8][9][10]12] as sample of this work.…”

Section: Introductionmentioning

confidence: 99%

On some general inequalities related to operator AM-GM inequality

Safshekan

Farokhinia

2020

Filomat

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“…The problem of squaring operator inequalities has been studied extensively in the literature. We refer the reader to [4,[8][9][10]12] as sample of this work.…”

Section: Introductionmentioning

confidence: 99%

On some general inequalities related to operator AM-GM inequality

Safshekan

Farokhinia

2020

Filomat

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Some refinements of young type inequality for positive linear map

Yang

Gao

2019

Mathematica Slovaca

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We obtain a refined Young type inequality in this paper. The conclusion is presented as follows: Let A, B ∈ B(𝓗) be two positive operators and p ∈ [0, 1], then $$\begin{array}{} \displaystyle A\sharp_p B+G^*(A\sharp_p B)G\le A\nabla_p B-2r(A\nabla B-A\sharp B), \end{array}$$ where r = min{p, 1 – p}, G = $\begin{array}{} \displaystyle \frac{\sqrt{L(2p)}}{2} \end{array}$ A–1S(A|B), L(t) is periodic with period one and L(t) = $\begin{array}{} \displaystyle \frac{t^2}{2}\left( \frac{1-t}{t} \right)^{2t} \end{array}$ for t ∈ [0, 1]. Moreover, we give the s-th powering of two inequalities related to the above one with s > 0 which refines Lin’s work. In the mean time, we present an inequality involving Hilbert-Schmidt norm.

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Improving some operator inequalities for positive linear maps

Yang¹,

Lu²

2018

Filomat

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Let 0 < mI ≤ A ≤ m I ≤ M I ≤ B ≤ MI and p ≥ 1. Then for every positive unital linear map Φ, Φ 2p (A∇ t B) ≤ (K(h,2) 4 1 p −1 (1+Q(t)(log M m) 2)) 2p Φ 2p (A t B) and Φ 2p (A∇ t B) ≤ (K(h,2) 4 1 p −1 (1+Q(t)(log M m) 2)) 2p (Φ(A) t Φ(B)) 2p , where t ∈ [0, 1], h = M m , K(h, 2) = (h+1) 2 4h , Q(t) = t 2 2 (1−t t) 2t and Q(0) = Q(1) = 0. Moreover, we give an improvement for the operator version of Wielandt inequality. where µ ∈ [0, 1]. When µ = 1 2 , we write A∇B and A B for brevity, respectively, see [1] for more details. The Kantorovich constant is defined by K(t, 2) = (t+1) 2 4t for t > 0. A linear map Φ : B(H) → B(H) is called positive (strictly positive) if Φ(A) ≥ 0 (Φ(A) > 0) whenever A ≥ 0 (A > 0), and Φ is said to be unital if Φ(I) = I.

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Complementary inequalities to improved AM-GM inequality

Abstract: Abstract. Following an idea of Lin, we prove that if A and B be two positive operators suchandwhereand h = M m and Φ is a positive unital linear map.

Cited by 3 publications

References 11 publications

On some general inequalities related to operator AM-GM inequality

On some general inequalities related to operator AM-GM inequality

Some refinements of young type inequality for positive linear map

Improving some operator inequalities for positive linear maps

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