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Full-Text Articles in Physical Sciences and Mathematics
Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications, Hamdullah Başaran, Mehmet Gürdal, Ayşe Nur Güncan
Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications, Hamdullah Başaran, Mehmet Gürdal, Ayşe Nur Güncan
Turkish Journal of Mathematics
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.
Some Results Related To The Berezin Number Inequalities, Ulaş Yamanci, Mübari̇z Tapdigoğlu
Some Results Related To The Berezin Number Inequalities, Ulaş Yamanci, Mübari̇z Tapdigoğlu
Turkish Journal of Mathematics
In this paper, we prove reverse inequalities for the so-called Berezin number of some operators. Also, by using the classical Jensen and Young inequalities, we obtain upper bounds for Berezin number of $A^{\alpha}XB^{\alpha}$ and $A^{\alpha}XB^{1-\alpha}$ for the case when $0\leq\alpha\leq1$.