Inequalities Involving Berezin Norm and Berezin Number

被引：23
|
作者：
Bhunia, Pintu [1 ]
Paul, Kallol [1 ]
Sen, Anirban [1 ]
机构：
[1] Jadavpur Univ, Dept Math, Kolkata 700032, West Bengal, India
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2023年 / 17卷 / 01期
关键词：
Berezin norm; Berezin number; Reproducing kernel Hilbert space; OPERATORS; SYMBOL;
D O I：
10.1007/s11785-022-01305-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We obtain new inequalities involving Berezin norm and Berezin number of bounded linear operators defined on a reproducing kernel Hilbert space H. Among many inequalities obtained here, it is shown that if A is a positive bounded linear operator on H, then ||A||(ber) = ber(A), where ||A||(ber) and ber(A) are the Berezin norm and Berezin number of A, respectively. In contrast to the numerical radius, this equality does not hold for selfadjoint operators, which highlights the necessity of studying Berezin number inequalities independently.
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页数：15
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