GENERALIZATION OF THE KANTOROVICH TYPE OPERATOR INEQUALITIES VIA GRAND FURUTA INEQUALITY

摘要

In this note we show the characterization of the S -order by means of a generalized Kantorovich constant via Grand Furuta inequality, which is an extension result of that from M. Fujii, E. Kamei and Y. Seo, Kantorovich type operator inequalities via grand Furuta inequality, Sci. Math., 3, (2000), 263-272. Among other, we show the following characterization of the S -order: Let A, B be positive invertible operators on a Hilbert space H satisfying MI ≥ A ≥ Mi > o and NI ≥ B ≥ nI > O. Then the following statements are mutually equivalent for each δ ∈ [0, 1].