Operator means and range inclusion (Q1190122)

\textit{F. Kubo} and \textit{T. Ando} [Math. Ann. 246, 205-224 (1980; Zbl 0412.47013)] defined an operator mean as a binary operation among positive operators satisfying axioms of monotonity, upper continuity, transformer inequality and normalization and established their general theory of operator means. The author [Math. Jap. 24, 459-462 (1979; Zbl 0435.47031)] has shown how initial conditions on the representing function \(f(x)=1mx\) for a symmetric operator mean \(m\) reflect kernel and range inclusion of means. This paper is devoted to extend these results to the case of nonsymmetric operator means.