Berezin number and Berezin norm inequalities for operator matrices

被引：9

作者：

Bhunia, Pintu ^{[1
]}

Sen, Anirban ^{[2
]}

Barik, Somdatta ^{[2
]}

Paul, Kallol ^{[2
,3
]}

机构：

[1] Indian Inst Sci, Dept Math, Bengaluru, India

[2] Jadavpur Univ, Dept Math, Kolkata, India

[3] Jadavpur Univ, Dept Math, Kolkata 700032, West Bengal, India

来源：

LINEAR & MULTILINEAR ALGEBRA | 2024年 / 72卷 / 16期

关键词：

Berezin norm; Berezin number; numerical radius; operator norm; reproducing kernel Hilbert space; NUMERICAL RADIUS INEQUALITIES; SYMBOL; BOUNDS;

D O I：

10.1080/03081087.2023.2299388

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish new upper bounds for the Berezin number andBerezin norm of operator matrices, which are refinements of existingbounds. Among other bounds, we prove that ifA=[Aij]isannxnoperator matrix withAij is an element of B(H)fori,j=1, 2,...,n, then & Vert;A & Vert;ber <=parallel to parallel to[& Vert;Aij & Vert;ber]parallel to parallel to andber(A)<= w([aij]),whereaii=ber(Aii),aij=parallel to parallel to|Aij|+|A & lowast;ji|parallel to parallel to 1/2ber parallel to parallel to|Aji|+|A & lowast;ij|parallel to parallel to 1/2berifij. We also provideexamples which illustrate these bounds for some concrete operatorsacting on the Hardy-Hilbert space

引用

页码：2749 / 2768

页数：20

共 43 条

[1] Numerical radius inequalities for n x n operator matrices [J].