Products of Toeplitz operators on the polydisk

被引：16

作者：

Ding, XH ^{[1
]}

机构：

[1] Guilin Inst Elect Technol, Dept Math, Guilin 541004, Peoples R China

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2003年 / 45卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Toeplitz operator; hardy space; polydisk;

D O I：

10.1007/s000200300013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper studies products of Toeplitz operators on the Hardy space of the polydisk. We show that TfTg = 0 if and only if TfTg is a finite rank if and only if T-f or T-g is zero. The product TfTg is still a Toeplitz operator if and only if there is a h is an element of L-infinity (T-n) such that TfTg - T-h is a finite rank operator. We also show that there are no compact simi-commutators with symbols pluriharmonic on the polydisk.

引用

页码：389 / 403

页数：15

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