Some results related to the Berezin number inequalities

YAMANCI U., Garayev M.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.4, pp.1940-1952, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1812-12
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1940-1952
  • Keywords: Berezin number, positive operator, reproducing kernel Hilbert space, Berezin symbol, McCarthy inequality, NUMERICAL RADIUS INEQUALITIES, REPRODUCING KERNELS, TOEPLITZ-OPERATORS, INVERTIBILITY, COMPACTNESS
  • Süleyman Demirel University Affiliated: Yes

Abstract

In this paper, we prove reverse inequalities for the so-called Berezin number of some operators. Also, by using the classical Jensen and Young inequalities, we obtain upper bounds for Berezin number of A(alpha) X B-alpha and A(alpha) X B1-alpha for the case when 0 <= alpha <= 1.