The new reverses of Young type inequalities for numbers, operators and matrices

Nasiri, Leila; Liao, Wenshi

doi:10.7153/oam-2018-12-64

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Cited by 3 publications

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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%

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%

New generalized inequalities using arbitrary operator means and their duals

Nasiri

Bakherad

2021

AUCMCS

Self Cite

View full text Add to dashboard Cite

show abstract

Reverses of Young Type Inequalities for Matrices Using the Classical Kantorovich Constant

Nasiri

Shakoori

2018

Results Math

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Some refined Young type inequalities using different weights

Nasiri

Askari

2021

Asian-European J. Math.

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The Young type inequality asserts that if [Formula: see text] are two positive real numbers, then for each [Formula: see text], we have [Formula: see text] In this paper, we obtain some new inequalities using two different weights. For example, if [Formula: see text], then [Formula: see text] [Formula: see text] where [Formula: see text] In addition, we refine some matrix inequalities for Unitarily invariant norms by applying the deduced numerical inequalities.

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The new reverses of Young type inequalities for numbers, operators and matrices

Abstract: In this note, we give reverses of Young inequality for numbers. Then we establish operator and matrix inequalities corresponding the obtained numerical inequalities.Mathematics subject classification (2010): 47A30, 15A42, 15A60.

Cited by 3 publications

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New generalized inequalities using arbitrary operator means and their duals

New generalized inequalities using arbitrary operator means and their duals

Reverses of Young Type Inequalities for Matrices Using the Classical Kantorovich Constant

Some refined Young type inequalities using different weights

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