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

页码：4353 / 4360

页数：8

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