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

  • Nəşrin Növü: Article / Article
  • Cild: 38 Say: 11
  • Nəşr tarixi: 2024
  • Doi nömrəsi: 10.2298/fil2411929t
  • jurnalın adı: FILOMAT
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.3929-3936
  • Adres: Bəli

Qısa məlumat

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.