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.
Reproducing kernel Hilbert space, Berezin symbol, Berezin number, positive operator, Hölder-McCarthy-type inequality, Kantorovich-type inequality, Heinz-Kato inequality
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