BEREZIN TRANSFORM OF PRODUCTS OF TOEPLITZ OPERATORS ON THE HARDY SPACE

被引：0

作者：

Xia, Jingbo ^{[1
]}

机构：

[1] SUNY Buffalo, Dept Math, Buffalo, NY 14260 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 152卷 / 10期

关键词：

Toeplitz operator; Berezin transform; LOCALIZATION; COMPACTNESS; ALGEBRA;

D O I：

10.1090/proc/16268

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let H-2(S) be the Hardy space on the unit sphere in C-n. We show that there are Toeplitz operators T-f and (T)g on H-2(S) such that the product TfTg is not compact and yet parallel to T(f)T(g)k(z)parallel to tends to 0 as vertical bar z vertical bar bar right arrow 1. Consequently, the Berezin transform < T(f)T(g)k(z), k(z)> tends to 0 as vertical bar z vertical bar bar right arrow 1.

引用

页码：4269 / 4276

页数：8

共 12 条

[1]

Aleksandrov A. B, 1982, Mat. Sb., V118, P147

[2]

Axler S, 1998, INDIANA U MATH J, V47, P387

[3] Compactness characterization of operators in the Toeplitz algebra of the Fock space Fαp [J].