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
@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},
}
%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
