Glasgow Mathematical Journal, ( ISI ), Volume (63), No (3), Year (2021-9) , Pages (622-639)

Title : ( VARIANTS OF ANDO–HIAI TYPE INEQUALITIES FOR DEFORMED MEANS AND APPLICATIONS )

Authors: Mohsen Kian , Mohammad Sal Moslehian , Yuki Seo ,

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Abstract

‎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.

Keywords

, Ando, , Hiai inequality; operator mean; deformed mean; operator power mean; Karcher mean; generalized Kantorovich constant; Specht ratio
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@article{paperid:1082226,
author = {Mohsen Kian and Sal Moslehian, Mohammad and Yuki Seo},
title = {VARIANTS OF ANDO–HIAI TYPE INEQUALITIES FOR DEFORMED MEANS AND APPLICATIONS},
journal = {Glasgow Mathematical Journal},
year = {2021},
volume = {63},
number = {3},
month = {September},
issn = {0017-0895},
pages = {622--639},
numpages = {17},
keywords = {Ando--Hiai inequality; operator mean; deformed mean; operator power mean; Karcher mean; generalized Kantorovich constant; Specht ratio},
}

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%0 Journal Article
%T VARIANTS OF ANDO–HIAI TYPE INEQUALITIES FOR DEFORMED MEANS AND APPLICATIONS
%A Mohsen Kian
%A Sal Moslehian, Mohammad
%A Yuki Seo
%J Glasgow Mathematical Journal
%@ 0017-0895
%D 2021

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