HARDY-HILBERT'S INEQUALITY AND POWER INEQUALITIES FOR BEREZIN NUMBERS OF OPERATORS

被引：42

作者：

Garayev, Mubariz T. ^{[1
]}

Gurdal, Mehmet ^{[2
]}

Okudan, Arzu ^{[2
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia

[2] Suleyman Demirel Univ, Dept Math, TR-32260 Isparta, Turkey

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2016年 / 19卷 / 03期

关键词：

Hardy inequality; Hardy-Hilbert inequality; Berezin symbol; Berezin number; positive operator; self-adjoint operator; REPRODUCING KERNELS; SPACES; SYMBOL;

D O I：

10.7153/mia-19-64

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give operator analogues of some classical inequalities, including Hardy and Hardy-Hilbert type inequalities for numbers. We apply these operator forms of such inequalities for proving some power inequalities for the so-called Berezin number of self-adjoint and positive operators acting on Reproducing Kernel Hilbert Spaces (RKHSs). More precisely, we prove that (ber(f(A)))(2) <= Cber ((f(A))(2)) for some constants C > 1. We also use reproducing kernels technique to estimate dist (A, U), where U is the set of all unitary operators on a RKHS H = H (Omega) over some set Omega, for some operator A on H (Omega).

引用

页码：883 / 891

页数：9