# The Furuta Inequality and an Operator Equation for Linear Operators

### Chia-Shiang Lin

Bishop’s University, Lennoxville (Quebec), Canada

## Abstract

*H__p*-2_rn_/2(*n*+1) *T* (*H__p*+2_r_/(*n*+1) *T*)*n* *H__p*-2_rn_/2(*n*+1) = *Kp*. This result also generalizes Lemma 1 in [3] which is about the operator equation *T* (_H_1/*n* *T*)*n* = *K*. A new characterization of the Löwner–Heinz formula and some applications are given.