Some Upper Bounds for the Berezin Number of Hilbert Space Operators

被引：18
|
作者：
Taghavi, Ali [1 ]
Roushan, Tahere Azimi [1 ]
Darvish, Vahid [2 ]
机构：
[1] Univ Mazandaran, Fac Math Sci, Dept Math, POB 47416-1468, Babol Sar, Iran
[2] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing, Jiangsu, Peoples R China
来源：
FILOMAT | 2019年 / 33卷 / 14期
关键词：
Berezin number; Numerical radius; Geometric mean; INEQUALITIES;
D O I：
10.2298/FIL1914353T
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we obtain some Berezin number inequalities based on the definition of Berezin symbol. Among other inequalities, we show that if A, B be positive definite operators in B(H), and A#B is the geometric mean of them, then ber(2)(A#B) <= ber(A(2)+B-2/2)-1/2 inf (lambda is an element of Omega )zeta((k) over cap (lambda)), where zeta((k) over cap (lambda)) = <(A - B)(k) over cap (lambda),(k) over cap (lambda)>(2), and (k) over cap (lambda) is the normalized reproducing kernel of the space H for lambda belong to some set Omega.
引用
收藏
页码：4353 / 4360
页数：8
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