Upper and lower bounds of the A-Berezin number of operators

HUBAN M. B.

Turkish Journal of Mathematics, vol.46, no.1, pp.189-206, 2022 (SCI-Expanded, Scopus, TRDizin) identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.3906/mat-2108-90
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.189-206
  • Keywords: A-berezin number, Berezin number, Berezin symbol, Positive operator, Reproducing kernel hilbert space, Semiinner product
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

Let A be a positive bounded linear operator acting on a complex Hilbert space H. Any positive operator A induces a semiinner product on H defined by (Formula Presented) For any T ∈ B (H(Ω)), its A-Berezin symbol e (Formula Presented) is defined on Ω by (Formula Presented), λ ∈ Ω, where (Formula Presented) is the normalized reproducing kernel of H. In this paper, we introduce the notions (A, r) -adjoint of operators and A-Berezin number of operators on the reproducing kernel Hilbert space and prove some upper and lower bounds of the A-Berezin numbers of operators. In particular, we show that (Formula Presented) where |sin|AT denotes the A-sinus of angle of T.