The Ando-Hiai inequalities for the solution of the generalized Karcher equation and related results

Yamazaki, Takeaki

doi:10.1016/j.jmaa.2019.06.036

Cited by 7 publications

(3 citation statements)

References 31 publications

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“…It is also called Cartan mean and Riemannian mean. Extensions of Ando-Hiai inequality to the Karcher mean and generalized Karcher mean are due to Yamazaki [99,100]. Other Ando-Hiai type inequalities have meanwhile been obtained.…”

Section: Ando-hiai Inequalitymentioning

confidence: 99%

Log-majorization Type Inequalities

Bebiano

Lemos

Soares

2022

Trends in Mathematics

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Several inequalities have been established in the context of Hilbert spaces operators or operators algebras. Our discussion will be limited to matrices. Important inequalities in mathematics and other sciences, such as Golden-Thompson inequality or von Neumann trace inequality, and extensions, are revisited. Our main goal is to emphasize the link between majorization theory and other relevant inequalities.

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Section: Ando-hiai Inequalitymentioning

confidence: 99%

Log-majorization Type Inequalities

Bebiano

Lemos

Soares

2022

Trends in Mathematics

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“…They discussed various Ando-Hiai type inequalities for deformed means. For more information on the deformed means, the readers are referred to [14,15,31].…”

Section: Introductionmentioning

confidence: 99%

Variants of Ando--Hiai type inequalities for deformed means and applications

Kian

Moslehian

Seo

2019

Preprint

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For an n-tuple of positive invertible operators on a Hilbert space, we present some variants of Ando-Hiai type inequalities for deformed means from an n-variable operator mean by an operator mean, which is related to the information monotonicity of a certain unital positive linear map. As an application, we investigate the monotonicity of the power mean from the deformed mean in terms of the generalized Kantorovich constants under the operator order. Moreover, we improve the norm inequality for the operator power means related to the Log-Euclidean mean in terms of the Specht ratio.

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“…They discussed various Ando-Hiai type inequalities for deformed means. For more information on the deformed means, the readers are referred to [14,15,33].…”

mentioning

confidence: 99%

Variants of Ando–hiai Type Inequalities for Deformed Means and Applications

2020

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For an n-tuple of positive invertible operators on a Hilbert space, we present some variants of Ando–Hiai type inequalities for deformed means from an n-variable operator mean by an operator mean, which is related to the information monotonicity of a certain unital positive linear map. As an application, we investigate the monotonicity of the power mean from the deformed mean in terms of the generalized Kantorovich constants under the operator order. Moreover, we improve the norm inequality for the operator power means related to the Log-Euclidean mean in terms of the Specht ratio.

show abstract

The Ando-Hiai inequalities for the solution of the generalized Karcher equation and related results

Cited by 7 publications

References 31 publications

Log-majorization Type Inequalities

Log-majorization Type Inequalities

Variants of Ando--Hiai type inequalities for deformed means and applications

Variants of Ando–hiai Type Inequalities for Deformed Means and Applications

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