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  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. 309–313DOI 10.2977/PRIMS/1195143954