Some operator inequalities associated with Kantorovich and Hölder-McCarthy inequalities and their applications

Authors: HAMDULLAH BAŞARAN, MEHMET GÜRDAL, AYŞE NUR GÜNCAN

Abstract: 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.

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

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