Numerical radius, Berezin number, and Berezin norm inequalities for sums of operators

Authors: NAJLA ALTWAIJRY, KAIS FEKI, NICUSOR MINCULETE

Abstract: The purpose of this article is to explore various inequalities pertaining to the numerical radius of operators in a Hilbert space. Additionally, we present several bounds for the Berezin number and Berezin norm of operators that act on a reproducing kernel Hilbert space. Finally, we establish a necessary and sufficient condition for the triangle inequality related to the Berezin number to hold.

Keywords: Sum, inequality, numerical radius, Berezin number, Berezin norm

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