Berezin number and Berezin norm inequalities for operator matrices

被引：6
|
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
收藏
页码：2749 / 2768
页数：20
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