A Note on Kantorovich and Ando Inequalities
Mohammad Sababheh, Hamid Reza Moradi, Ibrahim Halil G\"um\"u\c{s}, and, Shigeru Furuichi
TL;DR
This paper provides new proofs, refinements, and equivalent forms of Kantorovich and Ando inequalities, enhancing understanding and applications of these fundamental operator inequalities.
Contribution
It introduces a novel proof of Ando's inequality, a non-trivial refinement of Kantorovich inequality, and presents equivalent forms with Minkowski-type applications.
Findings
New proof of Ando's inequality
Refinement of Kantorovich inequality
Equivalent forms with Minkowski applications
Abstract
The main goal of this exposition is to present further analysis of the Kantorovich and Ando operator inequalities. In particular, a new proof of Ando's inequality is given, a new non-trivial refinement of Kantorovich inequality is shown, and some equivalent forms of Kantorovich inequality are presented with a Minkowski-type application.
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Taxonomy
TopicsMathematical Inequalities and Applications · Mathematics and Applications · Functional Equations Stability Results