New Refinement of the Operator Kantorovich Inequality

Hamid Moradi,Shigeru Furuichi,Zahra Heydarbeygi

doi:10.3390/math7020139

Abstract

We focus on the improvement of operator Kantorovich type inequalities. Among the consequences, we improve the main result of the paper [H.R. Moradi, I.H. Gümüş, Z. Heydarbeygi, A glimpse at the operator Kantorovich inequality, Linear Multilinear Algebra, doi:10.1080/03081087.2018.1441799].

Highlights

We focus on the improvement of operator Kantorovich type inequalities
Various attempts have been made by many authors to improve and generalize the operator Kantorovich inequality
In order to establish our promised refinement of the operator Kantorovich inequality, we use the well-known monotonicity principle for bounded self-adjoint operators on Hilbert space

Summary

Introduction

We focus on the improvement of operator Kantorovich type inequalities. Among the consequences, we improve the main result of the paper [H.R. At the beginning of this paper, we cite the following inequality which is called the operator Hilbert spaces throughout the paper) and A is a positive operator with spectrum contained in [m, M] with 0 < m < M. Various attempts have been made by many authors to improve and generalize the operator Kantorovich inequality.

Results

Conclusion