Some results for reproducing kernel Hilbert space operators via Berezin symbols

Tapdigoglu R., Garayev M.

FILOMAT, vol.38, no.11, pp.3929-3936, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 11
  • Publication Date: 2024
  • Doi Number: 10.2298/fil2411929t
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3929-3936
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

By applying the Berezin symbols method, we investigate the solvability of the Riccati operator equation XAX+XB-CX-D=0 on the set of operators of the form Toeplitz + compact on the Bergman space L-a(2)(D) of analytic functions in the unit disc D={z is an element of C:|z|<1}. We also characterize compact truncated operators on the standard reproducing kernel Hilbert space in the sense of Nordgren and Rosenthal. Moreover, we discuss solvability of the equation T phi 1X1+T phi 2X2+ ... +T phi nXn=I+K, where T-phi i (i=<(1,n)over bar>) is the Toeplitz operator on L-a(2)(D) and K:L-a(2)(D)-> L-a(2)(D) is a fixed compact operator.