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Inequalities involving Berezin norm and Berezin number of Hilbert space operators

Journal of Mathematical Inequalities
Summary: This paper presents several Berezin number and norm inequalities for Hilbert space operators. These inequalities improve some earlier related inequalities. Among other inequalities, it is shown that if \(A\) is a bounded linear operator on a Hilbert space, then \[ \mathbf{ber}^2(A) \leqslant \left\|\frac{A^\ast A + AA^\ast}{2} - \frac{1}{2R ...
Nikzat, Elham, Omidvar, Mohsen Erfanian
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An introduction of Berezin sectorial operators and its application to Berezin number inequalities

We introduce a new class of operators, called Berezin sectorial operators, which generalizes classical sectorial operators. We provide examples on the Hardy-Hilbert space showing that there exist operators that are Berezin sectorial but not sectorial and that the Berezin sectorial index can be strictly smaller than the classical one.
Mahapatra, Saikat +4 more
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On A-Berezin number in functional Hilbert space

Filomat
A-Berezin radius distance andA-Berezin norm distance are presented in this study. Furthermore, by employing the notions of A-Berezin radius distance and A-Berezin norm distance, we find A-Berezin radius inequalities of the product and commutator of functional Hilbert space operators. Moreover, we generalize the A-Berezin radius distance.
GÜRDAL, Mehmet, Başaran, Hamdullah
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Near infrared light controlled gene editing. [PDF]

Light Sci Appl
Berezin MY.
europepmc +1 more source

Lineage-Specific Disruption of Hematopoiesis by Oxaliplatin: Mechanisms of Erythropoietin Resistance and Immune Suppression. [PDF]