On some problems for reproducing Kernel Hilbert space operators via the Berezin transform

Official URL: https://dx.doi.org/10.1007/s00009-021-01926-y

We give some applications of Berezin transforms and Engliś C∗-algebras methods, namely we investigate the solution of generalized Riccati operator equation of the form XAX+∑i=1NBiXCi-D=0,N≥2via Berezin transforms. Also, we study finite product of operators, including finite zero-product of Toeplitz operators on the Bergman Hilbert space La2(D) in terms of Berezin transforms. The same method is used for characterization of compact truncated operators on the reproducing kernel Hilbert space H= H(Ω).