BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.47, no.4, 2024 (SCI-Expanded)
Let A be the 2 x 2 diagonal operator matrix determined by a positive Hilbert space operator A. We give several upper bounds for the A-Berezin number of 2 x 2 block matrices on a reproducing kernel Hilbert space and prove inequalities for the A-Berezin number of Hilbert space operators. Our results in this paper generalize and refine earlier the A-Berezin number inequalities.