We obtain new inequalities involving Berezin norm and number of bounded linear operators defined on a reproducing kernel Hilbert space $${\mathscr {H}}.$$ Among many obtained here, it is shown that if A positive operator {H}}$$ , then $$\Vert A\Vert _{ber}={{{\textbf {ber}}}}(A)$$ where _{ber}$$ $${{{\textbf are the A, respectively. In contrast to numerical radius, this equality does not hold f...

In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...