Improvements of Berezin number inequalities

Abstract

In this paper, we generalize several Berezin number inequalities involving product of operators, which acting on a Hilbert space H (Ω). Among other inequalities, it is shown that if A, B are positive operators and X is any operator, then ber r (H α (A, B)2010 Mathematics Subject Classification. Primary 47A30, Secondary 15A60, 30E20, 47A12 .

Some extended Berezin number inequalities

“…For our purpose, we set the Berezin norm of an operator as A ber supA kλ Therefore, the Berezin symbol uniquely determines the operator. Some excellent results about the Berezin number were found in [4,5,13,[25][26][27] very recently. Among many techniques in obtaining numerical radius and Berezin number inequalities is the study of certain scalar ones.…”

“…Once we finish studying the Euclidean Berezin number, we show a Berezin number inequality. Hajmohamadi et al [13] established that ber r A β XB 1β f X r berβA r 1 βB r inf…”

“…The objective of this paper is to present some results of Berezin number inequalities involving fconnection of operators. Finally, we present a generalized Euclidean Berezin number inequality and refine the inequality (13).…”

Operator inequalities in reproducing kernel Hilbert spaces

“…More information about numerical range and numerical radius can be found in [6,7,9,18,19,21]. Using the Hardy-Hilbert type inequalities and some well-known inequalities, some important results about the Berezin number inequalities were obtained in [2,3,10,22,[24][25][26][27][28].…”

Some results related to the Berezin number inequalities

“…More information about numerical range and numerical radius can be found in [1,4,14,19,21,24,25]. Recently, some results about the Berezin number were obtained in [3,18,20,29,30].…”