COMPLETE REFINEMENTS OF THE BEREZIN NUMBER INEQUALITIES

Bakherad M., Lashkaripour R., Hajmohamadi M., YAMANCI U.

JOURNAL OF MATHEMATICAL INEQUALITIES, vol.13, no.4, pp.1117-1128, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.7153/jmi-2019-13-79
  • Journal Name: JOURNAL OF MATHEMATICAL INEQUALITIES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1117-1128
  • Keywords: Berezin number, Berezin symbol, Heinz means, KERNEL HILBERT-SPACE, NUMERICAL RADIUS, OPERATORS
  • Süleyman Demirel University Affiliated: Yes

Abstract

In this paper, several refinements of the Berezin number inequalities are obtained. We generalize inequalities involving powers of the Berezin number for product of two operators acting on a reproducing kernel Hilbert space H = H(Omega) and also impmve them. Among other inequalities, it is shown that if A,B is an element of B(H) such that vertical bar A vertical bar B = B* vertical bar A vertical bar. f and g are nonnegative continuous functions on [0,infinity) satisfying f(t)g(t) = t (t >= 0). then