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VARIANTS OF ANDO–HIAI TYPE INEQUALITIES FOR DEFORMED MEANS AND APPLICATIONS

Part of: Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  17 August 2020

MOHSEN KIAN ,
MOHAMMAD SAL MOSLEHIAN  and
YUKI SEO
MOHSEN KIAN
Affiliation:
Department of Mathematics, University of Bojnord, P.O. Box 1339, Bojnord94531, Iran, e-mail: kian@ub.ac.ir
MOHAMMAD SAL MOSLEHIAN
Affiliation:
Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad91775, Iran, e-mails: moslehian@um.ac.ir; moslehian@yahoo.com
YUKI SEO
Affiliation:
Department of Mathematics Education, Osaka Kyoiku University, Asahigaoka, Kashiwara, Osaka582-8582, Japan, e-mail: yukis@cc.osaka-kyoiku.ac.jp
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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.

MSC classification

Primary: 47A64: Operator means, shorted operators, etc.
Secondary: 47A63: Operator inequalities 47B65: Positive operators and order-bounded operators
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 3 , September 2021 , pp. 622 - 639
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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