We prove analogs of certain operator inequalities, including Hölder-McCarthy inequality, Kantorovich inequality, and Heinz-Kato inequality, for positive operators on the Hilbert space in terms of the Berezin symbols and the Berezin number of operators on the reproducing kernel Hilbert space.
BAŞARAN, HAMDULLAH; GÜRDAL, MEHMET; and GÜNCAN, AYŞE NUR
"Some operator inequalities associated with Kantorovich and Hölder-McCarthyinequalities and their applications,"
Turkish Journal of Mathematics: Vol. 43:
1, Article 42.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/42