NEW UPPER BOUNDS RELATED TO THE BEREZIN NUMBER INEQUALITIES

. The Berezin symbol (cid:101) A of an operator A on the reproducing kernel Hilbert space H (Ω) over some set Ω with the reproducing kernel K λ is defined by The Berezin number of an operator A is defined by We study some problems of operator theory by using this bounded function (cid:101) A , including estimates for upper bounds for the Berezin numbers of some operators. We also establish some inequalities involving of the Berezin number inequalities.

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