# The Furuta Inequality and an Operator Equation for Linear Operators

### Chia-Shiang Lin

Bishop’s University, Lennoxville (Quebec), Canada

## Abstract

We show that a special form of the Futura inequality is equivalent to an operator equation $H_{2(n+1)p−2rn}T(H_{n1p+2r}T)_{n}H_{2(n+1)p−2n}=K_{p}$. 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.

## Cite this article

Chia-Shiang Lin, The Furuta Inequality and an Operator Equation for Linear Operators. Publ. Res. Inst. Math. Sci. 35 (1999), no. 2, pp. 309–313

DOI 10.2977/PRIMS/1195143954